I think it's more important to focus on is the rationality of enforcing copyright law against music captured in the background of a video. Fair use should be much more broad.
So long as the video isn't produced for profit, the producer isn't unfairly benefitting off the presence of the music in the video, and the quality of the audio doesn't compete with that of a commercial recording, I don't see the issue.
So long as the video isn't produced for profit, the producer isn't unfairly benefitting off the presence of the music in the video, and the quality of the audio doesn't compete with that of a commercial recording, I don't see the issue.