If it’s a rated tournament, and both players agree on a result, then my policy is to take that result even if I know it is incorrect. If someone agrees that he has been checkmated when in fact he hasn’t that’s his problem. In a rated tournament I expect that the players will know enough to recognize illegal moves, or to know what constitutes checkmate. If they don’t, then they probably should not be playing rated chess, and they will suffer the consequences.
If the result you gather is “who won” rather than “were you checkmated” then the lone king player saying that the opponent won has resigned. Sometimes pieces are accidentally moved after the game is over (or moved for analysis) before the TD arrives to collect the result and in those cases the questions actually are more accurate than the physical evidence.
Addendum. This afternoon I came upon a game where the SrTD/GM verified a checkmate even though the opponent looked to have NxR. When I asked later I learned that they had already started resetting the board, thus reinforcing that the board may not show the final position.
Agree. I never ask “were you checkmated” preferring something more open ended like “what was the result?” I find that that reduces but does not eliminate problematic answers from the youngsters. My policy is to always ask more follow up questions until I get a clear as possible understanding as to what the player is saying to trying to say. I do my best to remember my law school days and ask only non-leading questions that would be admissible.
In law school they teach litigators not to ask a question unless you already know the answer. So, you should already know the result before the kids come up to tell you! Seriously, the players need to be trained to know how to mark their score, whether it is on a pairing sheet or on a scoring slip. Announcements have to be made concerning scoring before the event to tell the players what to do. In large events, the TDs should have a scripted set of questions to ask the players before they finish marking the slips and signed them. Younger kids are easily confused, but can learn the process quickly with proper guidance.
When players disagree on a result, then they better have score sheets as evidence to prove their result. If players fail to mark the result, the typical thing is to chase them down wasting time and energy to find out. They learn pretty fast though when they get a double forfeit and have to ask to be let back into the tournament. That applies to stronger players, too, who wander off to analyze and fail to mark the pairing sheet, presuming that the TD knows their result.