I concur with most everyone here - it's an ingenious use of the skill, let him do it.
If it were my player, I'd throw him a bonus token. In my games, a bonus token means 'you did something that seems like it should be helpful, but I'm not sure it makes sense right now.' Later on, players can use bonus tokens to 'buy' other effects or advantages. Narratively speaking, it models a situation where a character's action doesn't have an immediate effect, but influences a future situation. This seems like the perfect situation for that - the constant questioning wears the victim down and, combined with other factors, causes him to accidently let slip a piece of information that the PCs didn't expect or weren't asking for, but is still very useful.