It's very important to be precise. Depending what country you're in, there could be full professors, assistant professors, associate professors, instructors, and other positions. Some of those positions might be well paid, but it's a safe bet that some of the others are not. So if you're looking at one full professor's salary and thinking that most other people with the word professor in their name make the same salary, depending what country you live in, you would be mistaken.
Actually wait a second, that's true in every country.
He doesn't need to prove it beyond a reasonable doubt. This is a civil suit. Essentially, his face value evidence is strong enough to win unless the hotel can provide clear explanation of how it did what it did, for example if they had different people processing different stacks of papers. At the same time, the plaintiff will have a chance for discovery, so who knows what will happen on that front.