I don’t think I’ll find a perfect example I’m afraid, just the key principles that underpinned other judgements.
With regards to the documentary example, I think that would come under “fair use” for the following reasons:
1. Transformative use (similar to news reporting)
2. Minimal impact on the market for resale/licensing.
However it’s worth noting in your example that folks are investing heavily in avoiding incidental copyright infringement (see for example dashcam footage on YouTube where songs on the radio are being either cut or pitched up/down or monetised to the rights holder rather than the publisher), which implies that folks cleverer than me, and probably with law degrees, at least see a risk of losing lawsuits over this kind of incidental infringement.
I appreciate that I pointed out that I can’t find a perfect example and then picked apart your imperfect example.
Maybe it’s best for everyone that there is no fully litigated perfect example of this?