One of the interesting things about this sort of dispute when I have seen it on the trains (where other customers are berated for having the incorrect ticket, but the customers protest that they were told they may use that train because theirs was cancelled), and what is on display in this thread from key industry insiders, is that train guards sometimes seem to take the view that their judgement is the most important thing about the situation.
The argument seems to be (and correct me here if I'm wrong) that the guard needs to have some kind of evidence that the customer is telling the truth, and that without it the story will not be believed, or will be judged at least more likely to be a lie than the truth.
Intriguingly, in Court the opposite is more likely to be true. If a witness statement is submitted to the Court, and if the statement seems reasonable in nature, and if the statement corroborates some other verifiable facts (for example 'my booked train x was cancelled' - this fact is very easily determined nowadays), a Judge is quite likely to accept it as being true. It is of course a serious criminal offence to submit a witness statement that contains anything that you know is not true. If there is no other contradictory evidence against such a witness statement (which there usually isn't), then it is quite likely that the Judge would rule in the customer's favour. Obviously it's better if something is written down. But you don't need something written down to assert that you are honest. The guard couldn't come to the Court and submit a witness statement saying 'I think the customer lied to me' with nothing further to add. Much would hinge on how reasonably the customer and the company seemed to have acted, though, and on the amount of the fare in question, and on how the Judge interprets the dispute (i.e. one person vs a large company with hundreds of millions of pounds annual turnover).
Still, while I used to think litigation was extreme, unreasonable and unnecessary, the more I have read on this forum about the way industry insiders view this sort of dispute, the more I think that only customers taking train companies to the County Court will focus their minds on what their legal and contractual obligations really are.
Ultimately: you are a large firm. Your customer is one individual. Accusing them of lying is both a seriously bad look and likely to be bad business. Why bother?