There's no reason to keep a dispute going if the traveller insists the ticket is valid. Take details of the ticket (withdraw if necessary) and get name & address. It should be that simple, but I guess some people like to abuse the power they have.
I agree that some people definitely abuse their power, but by the same token I'm not sure it can be quite that simple. I think a system where obviously invalid tickets are dealt with on a "name and address" basis would be horrendously inefficient. So it then of course becomes a question of what is "obvious" (and at some level we're back to employee competence and knowledge, after all).
"I will check" is clearly better than "this isn't valid". But there's a line to be drawn somewhere and things aren't quite as clear cut as they might seem.