SLF - ASSUMING it was a fully serviceable 737 (apart from the APU FDS) then I'm pretty sure most MELs would allow dispatch, especially on that route and I would probably have been happy to take it subject to no need for the APU
However, as explained, it is the Captain's decision. There may have been other factors involved in serviceability terms which they would not have bothered to explain to pax. I would suspect that any attempt to 'take the airline to court' for failure to transport you is doomed to expensive failure. I can assure you that in my opinion it would be unusual for anyone to refuse to fly that sector on those grounds alone, so there would almost certainly have been other issues involved. Let me give you one hypothetical example - one of the engine driven generators has been tripping off occasionally over the last few days with no obvious fault and a replacement is to be fitted that night - I would probably not take the aircraft. Indeed an engineer might not be willing to apply the MEL in that case anyway. Would you expect a detailed PA from the crew reading out all the Tech Log entries for the last week? The airline itself would be taking a close look at the decision in any case since it impacts them heavily.
In a nutshell, it is the Captain's responsibility IN LAW to ensure the a/c is fit for 'the intended flight' and that is YOUR protection. I would suggest leaving it there?