Well, my interpretation happens to agree with yours.
That's because the rule is the DM determines when the appropriate circumstances for hiding exist, and the number one circumstance given is that someone can not see you clearly. That means it's the DM's job to determine whether or not someone can see you clearly. The implied reasoning behind this, however, is that if someone can see you clearly then they know your location. I think that's what folks are missing.
Seen clearly is not the only circumstance in which hiding is inappropriate! You also need to stay quiet. That means you can't yell out, "Hey, I'm over here!", from behind your pillar and then take the Hide action. The circumstance of you making noise is not appropriate for hiding, because it gives away your location.
If the floor is dusty, and you make tracks as you move behind the pillar, you need to try to cover your tracks, because a trail of footprints leading to your location is a circumstance that is inappropriate for hiding. That's because it tells everyone where you are.
So that's at least three circumstances in which hiding is inappropriate, but those are just examples. What they all have in common is that under such circumstances your location is known. That's what makes them inappropriate. The DM is charged with determining whether other circumstances are appropriate or not.
I agree. But the issue here seems to be that the common English definition of hide is imprecise. It's clear to me (and it seems you would agree) from the context given by the rules, that when you hide, you are hiding your location in the same way you would hide your emotions, by keeping your location secret and unknown. If it is already known, that is an inappropriate circumstance.
I can understand if you are not going to reply given the reply-storm the thread has become.
i am not missing the implication of known location. i have repeated times and again that hiding is not some sort of trick that automatically makes everyone else in the world forget.
What i challenge in the interpretation are some points that, as you said, reach one critical point: Known location. Be it the fact that location is actually "known" and not "implied" and ending with knowledge of location as requirement, with other views in the middle.
A breakdown:
1) First is actual reading of "you can't hide if bla bla". The claim is that the meaning is just that. Taken at face value. This brings us to point number 2.
2) To be able to hide you need to make yourself somehow unable to be seen clearly. Cover, (Heavy) Obscurement, Invisibility are all good options - as are some special exceptions via abilities feats and whatnot. This is a prerequisite, not something that is part of the act of hiding.
3) Hiding does not require your position to be unknown. This ties to point 4, so please keep on reading before making a judgement. Nowhere in the rules for hiding there's an explicit requirement for hiding to have the position unknown. I said explicitly, mind you.
4) There are several places in the PHB where are specified interactions between circumstances/actions and hiding: what we have in the rules are "dos" and "donts" that are scattered around and that differ in wording and outcome between "your position becomes known", "requirements for hiding/moving around "stealthly" and "reasons why you are no longer hidden".
- There's in the movement section of the PHB the requirement for moving "stealthly": Do not stay in the open and travel at a slow pace. ( @seeb i reckon you said something different on one of your posts)
- In unseen attacker and targets we have that if you are hidden your location is given away when an attack hits or misses.
- We have in the Hiding section that we know you give away your position if you make some noise (of a sufficient level, like shouting or knocking down a vase)
- We know that you are no longer hiding if you are discovered or if you stop hiding. (hiding section)
- We know that to stay hidden you have to stay quiet. (hiding section)
- We know that you can still leave traces -duh, but specified for invisible people -
- We know that when you hide you can be noticed if you do not roll over passive perception.
- At start of combat, you can be perceived as a threat.
5) "Hidden" is described as "unseen and unheard" in the PHB. Hiding "makes you" hidden.
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On this reading we have this cases that allows you to hide: You are not clearly seen. Not being "clearly seen" includes "not being seen at all"
On this reading we have this cases of when you are no longer hiding: You are discovered, you stop hiding, you are no longer quiet.
We have one clear case of "no longer hidden" - you stop hiding.
We have another case of "no longer hidden" - you stop caring of being quiet.
The remaining is a simple "you are discovered". Which might or might not include "your position is known", since once again is not directly stated, but it surely covers the "you are seen" case.
So, for sure we have 3 causes: Sounds that are not quiet-level, clear sight and will from the hidden person.
Before the main issue (position = known... i know, spoilers

) let's tackle another anomaly... You are noticed.
This means that, somehow, the noticing person is aware of presence. We do not know the extent, but we know for sure that is enough to prevent surprise rounds. We do not know how, and DM adjudication establish what goes wrong. It might be a guard hearing a tingle from the money in the pouch: "what was that?" if it's impossible for the guard to see the person hiding. This would probably end up with search checks and prehaps a "guess it was nothing" if those searches are unfruitful.
It might be an arrow bulging out from a bush, prompting a charge at said leavy coverage and subsequent discovery of an armed elf.
It might entail EVERY situation.
In short: not helping.
Position, on the other hand, as read means... position. If there are reasons for the person hiding to still not be heard and seen, then the position must be the only thing known, as "hidden = unseen and unheard".
A sniper shooting from afar and from the shadows is a perfect example: Too far for the twang to be heard, too dark to be clearly seen. Still hidden. But the recieving end of the attack knows the direction of the attack and has an idea from where such attack is coming from. How? In the same way as what motions you do/words you say while casting Magic Missile. DM adjudication.
It means that the having the position is not a reason alone to break hiding.
Then: If it's not a sufficient reason to break hiding, and it's not a reason to impede hiding... why make it so?
There are TONS of rules and examples of spells, actions and whatnot requiring SIGHT, not just any sense. Why should something whose requirement is explicit in mentioning direct sight require something else?
Doubly so, why pointing on something that is not a requirement as the reason for denying when denying is a DM right just because the very rule requires adjudication every single time? You said it so... DM adjudication is the reason. Not because the rules say so.
Explaining "why" that decision at the player is going to be difficult, however, since the ones being sure of location are only the humans at the table and the one behind the pillar. The characters are NOT sure. They can think that there's no other way, but have no proof. Discovery is what marks the end.
On your examples: Shouting has the same problem as moving behind the pillar: Having the position unknown is not a requirement. Hiding is a way to make your position unknown, being able to hide when your position is unknown is a corollary.Having it the other way also destroys the idea of sequence of actions. It prevents possible fun interactions (i shout behind the pillar, cast something, hide, trigger a previously placed magic mouth on the other side of the hallway. i know, specific. The point is it would be infeasible. You would need to admit that the situation could call for a reality check on what the onlooker actually know and what they think they know - something the master should always apply.)
On the dust: I'm not trying to hide going to the pillar. I'm hiding BEHIND the pillar. Order of actions. Btw, not Actions, like in combat ones. Just actions, things you do. It does not matter how i reach the point where i hide for determining if i'm hidden or not. It is helpful to remain hidden. To not give away my location. And again, no one is saying that if there's no way of escape this is a smart move. It's simply possible, as much as is for a fighter to chose and stab himself with a branch. The consequence is that you are unseen and unheard... and still neck deep in sheep.
If this wasn't true than no "misleading footsteps" situation would EVER work.
And yes. You say inappropriate. Not impossible. That is the whole point.
And i'm fine with: It's how it's adjudicated. I just do not agree.
Problem lays in confusing adjudication with RAW and RAI, while also bringing in twitter in the discussion while said tweets bring nothing to the table. All without providing full citations of the matter and trying to pass something as "clear" or "logical" with nothing but questionable reasoning.
And to add: If the person behind the pillar thinks he can hide, he'll try. He might be non the wiser of someone following him while hidden. You SHOULD let him roll, even if it's impossible, as much as you should let roll the attack of someone guessing a location incorrectly and then announcing the result as a miss. It's due to how people perceive the world, their knowledge of it. Their point of view. The other job of a DM is describing what is happening in a way that let the players choose what is best with informations they have availlable. Being permissive usually end up with more unexpected questions. Silly usually, but that is how you really have fun, memorable moments.