I'm pretty sure big media considers fair use an obscene concept, but I don't really see how is that relevant, since I didn't say ten seconds of a song should become fair use.

I was extending an assumption based off:

"not going after people who are just distributing ten second excerpts"

You are forgetting to account for context.

I was saying that they couldn't go if they can't afford to lose ten grand if they're wrong about the song, not that it'd be illegal to do so.