My experiences as both player and GM have been very different than that. I find that there can often be such discrepancies in understanding the shared fiction of the game. And yes, asking questions is part of the process of clarifying. But I would say so is sharing as much information as possible, and simply not worrying so much about the player-character division of information.
I mean, if having a shred of information that your character may not have is enough to shatter your sense of immersion or inhabitation, then I can't see how things like discussing hit points or rolling dice won't similarly take you right out of play. Hence my suggestion to accept that this happens, and then proceed with that idea in mind... and focusing less on situations that rely on that information.
As a very basic example... I stopped worrying about monster vulnerabilities for the vast majority of monsters in about 1988. Trolls and fire, vampires and garlic, lycanthropes and silver, and on and on.... I just am not interested in keeping those details from the players. Especially when most of them know it all already. So I don't let my games focus on "finding" the vulnerability.
Removing that kind of dreck actually lets me focus on things I expect my players will find far more interesting.