First off, apologies to all if this is ground already covered - I was called in on page 81 here and am not about to go over the previous 80 to find out what I've missed...
A hard rule (a.k.a. an actual rule) is explicit, either allowing or disallowing (or both) something(s) specific to happen in the play of a game.
"A king can move up to one square in any direction" is a hard rule: it allows a king to move one square and disallows it from moving any further. "Constitution 16 gives a bonus 3 hit points per character level" is a hard rule: it allows exactly that bonus and disallows any greater or lesser bonus. "A player on the attacking team may not precede the puck across the defensive team's blue line" is a hard rule: it disallows certain player positionings on the ice in certain situations.
Contrast this with "the objective of the game of hockey is to win via scoring more goals than the opposing team" which, while in the rulebook, neither specifically allows nor disallows anything. It's simply a guideline or suggestion as to how to play and not a rule at all until harder-coded into actual rules that define the win condition, define what a goal is and how it is scored, define the length of a game, and so on. And even then that guideline can still be ignored; a badly-overmatched team, for example, might take a different approach and instead of playing to try to win will instead play purely defensively, and try to lose by as small a margin as it can.
"Play to find out" falls into this same category - it neither specifically allows nor disallows anything and thus is not a rule: it's a guideline.
In hockey (and most other sports), each league has its own minor variants on an otherwise fairly-consistent set of rules; but in the end the league sets the (hard-coded) rules. Chess doesn't often even have that much variability, nor do most boardgames, card games, etc.
TTRPGs, however, are a different animal. Here, while the publisher might want to play the role of the league and set the hard rules*, there's these annoying things called GMs and players who - in the fine well-established tradition of RPG rules-kitbashing - want to make the game their own by taking those hard rules and in some cases putting them through a blender. And so, the role of the "league" falls on the GM (and players, maybe) at each table; to - to some degree - set the hard rules they're willing to play by and then play the game.
And some publishers realize this, and so rather than hard-coding lots of rules they give guidelines and suggestions, backed up by a far lesser amount of hard-coded rules. These guidelines are by nature a bit fuzzy, and that fuzziness makes them harder to change to any extent without (ntentionally or otherwise) changing the underlying foundation of the game as designed.
* - worth noting that most of these hard rules are dealing with quantifications and-or abstractions of those parts of the fiction that cannot be roleplayed in meat-space.
I think the above implies a far greater amount of "flaky GM whim" than I'm getting at. That said, IMO someone - be it the publisher, the GM, the table as a whole, or whoever - has to take on the role of "the league" and set the hard rules. And if all the publisher gives you is guidelines and expects them to be taken as hard rules, that doesn't seem to provide much help with the nitty-gritty of sorting those fictional abstractions; instead it shuts that responsibility on to some combination of the GM and players and asks them to figure it out for themselves.
And sure, if you've a table of agreeable not-competitive people willing to help with that figuring-out process on an ongoing basis this set-up could be great. My experience, however, is that a) some people tend to be more stubborn and-or competitive than that, and b) some - generally the more casual types - aren't willing to help with that figure-it-out process and would prefer the game do it for them.
Game mechanics are usually a fairly basic input-->processing-->output sequence. Most of the time the players provide the input(1), the game does the processing(2a) and gives output(2b), and the GM interprets that output and adds it to the fiction(3).
1. Player input: Action declaration "We search the room carefully, looking for any sign the princess was ever here."
2a. Processing: (meat-space game mechanics occur e.g. rolling of dice, checking of notes, or whatever the system in use asks for)
2b. Output: (meat-space game mechanics determine a result - let's say success in this case - which must be honoured in step 3)
3. Interpretation: GM narration "Tolbert, you find a few long blonde hairs caught in the window sash that roughly match what you'd expect to be the princess'; and Jerelle, you notice a stain on the floor - could be spilled tea - that can't be more than a few days old."
This on its own doesn't seem controversial. So where's the controversy? Is it the specifics around 2a? Is it lack of honouring the result in 2b? Is it that the GM gets to do the interpretation in step 3?
