Bedrockgames
I post in the voice of Christopher Walken
It started with you rejecting that as a description of another poster's play who - it turns out, unsurprisingly - may or may not play the same as you do.
No one in the history of mainstream RPGing has ever set out to create an unbelievable world. The "our side"/"your side" phrasing is nonsense, both in this case and in general (see my previous paragraph in this post).
There are complexities, though. Do you think X2 is a believable world? White Plume Mountain? Keep on the Borderlands? And of course Toon players do want a cartoony world, but I don't think anyone posting in this thread is a Toon player, and I seem to be the only poster who has played The Dying Earth and only for one session.
If players in WPM want to surf doors removed from hinges down the frictionless corridor to avoid the super-tetanus pits, and one of them pulls out a first year physics text to help with the velocity and momentum calculations, is that fair game?
In my Classic Traveller game we needed to decide how long it would take the PCs to drill and blast through 4 km of ice with a triple beam laser. The time mattered because it generates resource costs - especially fuel and salaries - and it also matters to what else might happen in the rest of the galaxy (the "living, breathing" world). As a group we Googled some stuff (published papers on using lasers to melt ice) and reached a consensus. Do you have any objection to that procedure? Is it is distinctive of "my side"? And what, if anything, does it tell us about the use of the GM's notes in play?
(More relevant might be who got to decide the alien complex is buried in 4 km of ice? Answer: me, the GM. Why? It's a component of framing, along with the fact that the planet was much colder than it had been 2 billion years ago when the aliens lived there, due to changes in the energy output of its star. How did I make the decision? I looked up the thickness of Antarctic ice and doubled it, because I wanted really thick ice.)
Part of the problem is you are focused on believability which is just one aspect of what I am talking about. If it turns out we don't actually disagree about anything, I would certainly welcome that. But you push back enough against my thoughts on sandbox, living world, sometimes even telling me what I say I am doing is an impossibility, that I think we must disagree here. The point of living world isn't just to make a believable world, but to make a world that is moving around the characters and feels external to them. The living part means the NPCs for example are not tethered to a particular place, are acting like PCs and doing things, responding to the players, etc. And this kind of thing, when you play it out, can produce a very consistent world experience (the players kill Scholar Han's wife; scholar Han goes to Iron God Meng then next day and hires him and his men to help track down and kill the PCs; The PCs learn Iron God Meng is after them and try to negotiate with him, outbidding Scholar Han; humiliated once again, Scholar Han decides to go into seclusion and try to achieve a martial arts break through so he is powerful enough to take on the party himself, etc)