The question has come up before so I just wanted to clarify our stance:
We, Subset Games, hereby declare that all YouTube users have our permission to run advertisements for the purpose of monetization on their videos of our game, FTL: Faster Than Light.
- Justin Ma & Matthew Davis (founders)
Hopefully that is sufficient evidence for them. Thanks!
EDIT: This also applies to other video services besides YouTube, such as, but not limited to, Twitch.tv.