There are two problems here:
1. Who has the rights to decide what goes into the game
2. What part of the delivered music will be paid.
I am not naive. If a musician contacts you and shows you good demos then you are inclined to believe this is his level or art. If the actual work then consists of some uncreative drum-loops from a music recording magazine CD and uninspired e-guitar solos on top you are fooled.
This means the problem is likely to go away if you know the composer and his work. If you trust the person, based on good reasons, then I see no problem to let the composer decide what is good what is bad and what goes in the game and what will be paid.
In this case I, as a composer, would expect to decide myself. If we agree on 5 tracks a 3 minutes before I start and in the end you want only 4 because your budget shrunk... either it is the producers problem or we negotiate something else for compensation, working around the money problem. I don't see real practical problems here.
Back to the fraud composer:
Although I think it is theoretically possible to rate music and art objectively this is very hard in practice.
a) There is technical quality. Right formats, clean recordings, no distortion or clipping. If you got a cheater-composer maybe he is amateurish enough to get these things wrong. There are many technical things which are related directly to the workflow and style, more than meets the eye/ear. For example someone who works with compressed (mp3) samples and delivers you a wave. If you compress that again you will get audible compression artifacts. This is a reason to not accept the work. Technical quality not met.
b)In case you are not satisfied with the music itself, and the composer is a person who does not listen to "I don't like this part, could you please work on it again".
If you, and others, have the feeling that the music does not hold up to the promised quality this usually has objective, measurable reasons. It is not so subjective at all to rate music. What many producers lack, of course, is the education to analyze the reasons why they don't like a piece and to find the right word. In that case get a second opinion. Find a musician and composer whose hearing is trained and who knows a lot about music theory. These are the people which can say objectively why them music you got suckz
In other words:
If you work with a suspicious composer and you've managed to make a contract that you only accept music which fits the overall quality of the game (and you a fair producer!) then it is absolutely possible to actually analyze the quality and reject music based on that. But that is work itself.