I didn't make any assertion about other people's styles, and I use a variety myself, depending on various factors, like I just said.
You did, you said, "If I had said "Don't roll" then they wouldn't have attempted to open the door or wouldn't have received the information that the door was incredibly hard to break." Given the discussion is on a style that says "don't roll" if the task is impossible, it's hard to read that as not making an assumption about that style. Context matters, here. Maybe it was a poor choice of phrasing on your part, I can see that, I've made many such myself, but you most certainly phrased it in a way that is naturally taken as speaking about styles were "don't roll for impossible tasks" is a thing.
That you carried that into a negation of action is even more concerning. It shows a broad lack of understanding about the principles involved in the style under discussion.
With the door, it was not literally unbreakable, a sufficiently high number could have broken it. For me to say "Don't roll" I would have had to first establish what the PC's maximum bonus was. Rather than have that discussion followed by you-bounce-off, for me it worked better to have player roll. It actually made for a dramatic little vignette - "No normal door could have withstood that!" Conversely with the high level Barbarians IMC I know what their minimum Athletics checks are (= STR, currently 24 & 30!) - so I will say "That was a DC 25 so you auto-succeed..." and that works well there, too.
It's fair that you don't have your player's stats memorized (although a DC 25+ door seems a bit obvious). However, that's not the point of not asking for a roll if the task is impossible or there is no consequence for failure. Here, it's pretty obvious there was no consequence for failure because you just provided information that it didn't work. Granted, that bit of information on this door showed players that it was impossible to bash, but that's not a consequence of the roll, but a consequence of that specific result. Had the result been less the a natural 20, the consequence would have been the same -- none. In this case, under my style, I would not ask for a roll, but still provide information to the party. The mistake often made in criticizing my style by those not familiar with it is that it still runs like yours -- you use rolls to convey information, I just provide the information. In the case of this door, I would have done as [MENTION=97077]iserith[/MENTION] did, and narrate as part of the description of the door that it looks nigh-unbreakable, that serious power outside the party's current ken was needed. Or, I, alternatively, would have done as I said above -- narrated the automatic failure of the action by providing all of the information you did on a natural 20. The lack of a roll doesn't mean nothing happens and the players are left with no new information. This is the assumption that comes from your style, where the roll is used to convey such, and which you assume, then, doesn't happen when no roll is made. That's not it, though, because the action is still attempted, and whatever outcome of that action obtains -- either auto-success/failure or a die roll -- information is still conveyed in the outcome that gives players necessary information to move forward in the game.
Conversely, I while I don't get the nice vignette of the natural 20 showing that the current task is beyond the strongest in the party (and I'm agreeing that's a fun outcome), I also don't have the frustration of rolling a 19 instead and wondering if it's worth it to keep trying for the 20. I recall that from my days using that style, and that's one of the reasons I switched -- that result was unsatisfying to me. If it works for you, awesome, I am legitimately glad this is so.
IMO the important thing with the 5e system is to be flexible, not doctrinaire, and use the best tools for the job.
I completely agree - doctrinaire styles really suck the wind out of the game. I'm very glad that neither I nor [MENTION=97077]iserith[/MENTION] use such a style, and also glad that you do not as well. We're all a very happy, non-doctrinaire party of gamers, yeah?