Is it not correct to say "לא היו לו מים"? On the other hand, that is what I understand in the audio too...
you are correct, however it is not wrong to say לא היה לו מים since water in hebrew like in english is an uncountable noun. The difference is you CAN use it in hebrew as a plural noun. so both לא היה and לא היו are ok.
Earlier it said he passed out because she told him to leave, and now he is trying to change the story... too late, we already know the truth.
My answer 'He didn't have any water, so he fainted' was marked incorrect. I'd say my answer sounds more natural in English, and it means the same thing. It isn't necessarily emphatic here; it just sounds more natural.