I would not even ask the questions, “Is it check? Can you find a move that gets you out of check?” I would throw it back on the player. My response will be, “What do you think? Why?” Anything else might be viewed as helping the player. The player must see it for himself and understand the position as it is. For younger players, this is a learning experience. For the older, veteran player, this should be enough for him to look at the position once again.
In many scholastic tournaments, the kids call you over to confirm the checkmate. You could say yes or no. I prefer to ask the other player, “Do you agree?” If he says yes, game over. If he says no, but it is a checkmate, then you turn to player A and say, “Show why you think it is a checkmate.” They both learn to look more closely. Usually both kids know the game is over, but just want a confirmation. I think some coaches tell them to do that. If this is a major tournament where there are signing slips, they both sign and the result is recorded. Otherwise, I tell them both to go over to mark the result correctly on the pairing sheet.
I can see it now. Players A & B play. B resigns. They walk to the results sheet, B trailing. A marks the result and leaves. B reneges on the result and restarts A’s clock who then loses on time…
I haven’t put my finger on it - but there is another niggling harm rolling around in my head, and its brought up by your hypothetical. Just when does the game end? What if, horrors, neither player marks a result and the TD says: “Does anyone know who won the game between A and B?” And now S says “A won”. Then, after the next round, A is analyzing (with B? with S?) and it is found there was no mate - and B protests?
This can easily get convoluted.
There was no intent at deception, and the players showed a meeting of the minds. A made an error, and so did B. They happen to be meta errors, but they determined a result.
Oddly (and perhaps Tim Just recalls this) many years ago I was playing Jesse Kraai in a tournament in the northern IL area - long before Jesse became a GM. We were in a mutual time scramble, the game was being watched by National Master Ken Wallach. I was chasing Jesse’s King, and announced “CHECK…(pause) …WAIT… MATE”. Jesse looked hurriedly – “What? What? No wait,…” then moving out of check (was it a capture, I can’t recall) he said “Hey, you can’t do THAT!”. I’m not sure why, but in the haste of the moment I replied “Well, I can, but I can be wrong.”