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: 
The sentence

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> Since the train was delayed for more than an hour, passengers were given a full refund.
> 
> 
> 

is formally ambiguous. One cannot tell from the sentence alone whether **the** passengers were given a refund -- that is, all the passengers -- or whether only **some** passengers were given a refund: perhaps only those who complained. When an article is elided in this way, the reader must determine from context and common sense what the meaning is, and which article is implied. Here either choice is possible, although "the" seems more likely. But in another context the result would be different.

> 
> After the minister's eulogy, friends and family spoke about the deceased.
> 
> 
> 

Does that mean that every one of the dead person's friends and family spoke, or only some of them? Were all of them even present? "Some" is the likely choice here, but further context could change that.

> 
> After the minister's eulogy, friends and family spoke about the deceased -- all five who were still alive.
> 
> 
> 

Now the implication is otherwise.

When the choice of article is obvious, omitting it does not mislead the reader. When there is more than one serious possibility, this may be poor writing. Or it may be intentionally ambiguous writing.
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.