An TV news programs aren't? I don't think the fair use doctrine distinguishes between profit and non-profits; and it is a documentary film. Can you show the law that says a for-profit cannot assert a fair-use defense?
Besides, you said it wouldn't make a profit.
Look up copyright law. Movies are expressly named as requiring a license. Why did they get licenses for the other music in the “documentary”. And no, it won’t make a profit.