What I don't think you're allowed to do is say 'no problem, can't be anything to do with your car crash' when what you mean is 'your skull is not fractured'.

That example only works because fractures are involved in a subset of car crashes and car crashes are involved in a subset of fractures; either one can happen without the other. If that relation doesn't hold true, you would be allowed to say that. For instance, saying "no problem, can't be anything to do with your car crash' when what you mean is 'you weren't anywhere near a car at the time of the crash'.