Clearly an ideal system would never reject a valid claim, but this is not reasonable, all systems have their limitations.
What is reasonable?
System A : Everything Manual, a human looks at the claim, they have extensive knowledge of the ticketing system, they have all the relevant running data, they read the notes you added and take this into account and make a decision.
System B : If it's absolutely clear cut, for example a single train being 68 minutes late to its destination, the automated system pays out, if it is more complicated than that, or the system is unsure, pass it straight on to a human with the knowledge, experience and data access as above to make a decision.
System C : If it's absolutely clear cut, for example a single train being 68 minutes late to its destination, the automated system pays out, if it is more complicated than that, sod that for a game of soldiers, just reject it outright and see if the passenger complains. If they do, let a human with a mere fraction of the above knowledge, experience and access to data have a look at it and be too scared to approve it so just copy and paste what the flawed automated system says and see if the passenger appeals a second time. If they do, let someone who has seen a rail ticket before have a look. If they don't appeal after the automated rejection, Christmas party fund.
A is, in my opinion the worst option, it would be frightfully slow and inefficient. Operators would want to pay very little and would provide next to no training meaning staff would likely default to rejection for fear of being reprimanded for giving out money.
B is, in my opinion the best of both, you have the automated system for speed, and you have the human for complications.
C is, the railway.
I've had claims rejected in the past when SWR used the time the train passed a signal a few miles away as the arrival time at my local station. Only when I pushed them they claimed it took 3 minutes to cover the 6 and a bit miles something which is impossible on a sprinter!
Indeed, although the automated system uses the data it is given, and of course, if a human looks at it they too can only go on the numbers in front of them so this sort of thing is difficult to get around.