From casually following along, it appears to me the "changing of reality" comes down to what people are defining as "reality" in the first place.
Some people seem to be saying that only things that have been declared is actually "real". That's the reality the characters are in. If the DM has not specifically made mention of a blacksmith in town, then the "reality" of the situation is that a blacksmith in town doesn't exist (yet.) If and when the DM OR a player makes mention of "going to see the blacksmith"... the "reality" is being ALTERED from a world where there was no blacksmith in this town to one where there is.
The other side being those folks here who are reading the idea of the change of the "game's reality" to be more about CONTRADICTING something having already been established. Adding something new that had not yet been defined is not "changing" by their way of thinking... but rather deciding by fiat that something that had been defined one way is now something different is "changing".
Until everyone is willing to accept either definition as the "correct" one for this discussion... there will never be agreement.
Is going from nothing to something a "changing of the game's reality" or is only something becoming something else a "changing of the game's reality"? Decide on that definition first and the discussion can probably continue on its course.
A hardline stance against
any form of filling empty spaces is impossible--it would certainly make GMing impossible. There are, of course, poor ways of using this ability e.g. railroading, but if every GM were required to have every "empty" space perfectly filled before people ever sit down for the first session, no one would play. But the same goes for every character! We know that they must have had parents, yet those parents do not need to be strictly defined. We know they must have had a childhood, which entails things like friendships and the little (mis)adventures of youth. If you're playing a game with classes, they had to learn those abilities. Etc. Few games require absolute specificity about these things, because again, if you were required to produce Tolkien-level notes on the culture, fashion, language, religion, family history, cuisine, etc., etc. of every single character you play, people wouldn't play.
It seems clear to me that the real issue is, people are very adverse to anything which can be parsed as declaring an advantage simply because. You can make attempts at things, and you can declare context, but you can't write "this is just what happened, which is beneficial to me." That's why 99.9% of the time when people balk at this, they very specifically bring up that players are using it to their advantage. You wouldn't see such a strenuously repeated refrain unless it mattered.
it is in fact the third possibility that we are primarily caught up on of Conan being able to point at 'random Set priest #6' and declare "that's them, that's Thulsa Doom, i know Thulsa Doom from my backstory and i know they have XYZ traits" and thus Priest #6 becomes Thulsa Doom with XYZ traits.
Priest #6 becoming Thulsa or the contents of the room the player 'remembers', they're the same as Oofta's example, you can't 'remember' money into your bank account because there should already be a certain amount of money in your account, even if you don't know how much that is.
And I'm saying
I've never played a game that lets you do that.
Spout Lore? You pick only what you're researching, and you
only get what the GM considers "interesting and useful," with the "and useful" part only if you roll well. You cannot just declare what you want to be true. The only thing you have any control over, and that only if the GM actually asks, is where/when you learned that information. (Generally, I don't ask if the answer is "these books I just finished poring over"; it's only if the answer is actually a lived experience where it's worth asking.)
In fact, let's take a look at those Flashbacks, shall we? As I said, I've never played or even really
looked at BitD, so I couldn't comment on them. I haven't played it in the last few hours, but I went looking. And it seems to me that, as usual, there's rather an overblown response here. Limitations and context are conveniently ignored or unstated and the actual, direct utility is exaggerated, rather a lot in fact.
So, with BitD, the game is centered on heisting. That's the goal. It's fantasy tabletop Payday. But the authors, rather candidly, note that one of the weaknesses of early-edition games (which were a heavy inspiration here) is that the "planning" part of a heist can sometimes be
several times longer than the actual "playing" part, and a lot of that time and effort is spent doing or preparing things that are simply irrelevant. This is, in the author's eyes, rather unfortunate. It means that you get a low proportion of actually doing heisty adventures, and a high proportion of wasteful, and often out-of-character, faffing about.
Instead, BitD says: "You did some preparation work.
We'll talk about that later. For now--ACTION." The preparation work explicitly already did happen. It's not a pluripotent thing; it must fit within reasonable established bounds. Hence, it is not, as so many are keen to suggest, a blank check for rewriting the world to whatever you want it to be. It is a "this space intentionally left blank" section that is meant to be revisited later.
Secondly, invoking a Flashback has a cost, specifically, Stress, which are effectively your HP. You only get 9 Stress to start (a thing rather inconveniently
not described in the actual BitD rules,
only visible in the character sheets), and with effort you can potentially get 11 total. If you max out your Stress, you're out for at least that scene, possibly the whole Score (the BitD term for each heist). Stress is also how you resist damage and various other things, so it's a precious resource.
Third, and most important,
invoking a Flashback DOES NOT just give you something nice. It gives you the opportunity to find out if you have something nice or not. Once the Flashback starts, the player must actually roleplay through the process of earning their benefit--just as would happen if all the prep-work scenes were done in advance. The only thing that changes is the order the group witnesses the events, and that order is specifically shifted because it makes for a better, more interesting experience and narrative.
So, no, I'm not even going to accept Flashbacks as an example here. They're costly, done solely to produce a more enriching experience, and absolutely
do not just let the player fiat declare their lives are happy happy joy joy forever. All they do is shuffle prep work scenes to a later point of the experience. That's it.