Question: After all, we are talking about very definite passengers – the ones that were on that train. Can it be gathered from the sentence that not all of the passengers were given a refund? 

P.S. The sentence comes from a grammar book.

Answer: 
It could be a stylistic reason, because "the" has already been used for "the train", so "passengers" reads better. It is possibly from a newspaper article. Your reasoning is correct, the refund concerns these specific passengers.
The main takeaway (for me) from reading that sentence is that the railway company admitted responsibility for the delay, and followed through on that admission by actually giving out full refunds. Who exactly got those refunds (all passengers, or just some passengers), and what they had to do in order to get them isn't part of the information that that sentence is trying to convey. Therefore it is left unspecific.