OK, what is "it" in this instance?? Because I'm starting to get the feeling that we're not on the same page.
I was thinking more along the lines of "you can't legally use our music in the background of your class project video because you're supposed to have our legal permission, and if enough people hear about it and we find out then we'll totally go after you".
Not "you can't hum or sing our music in your class project video, etc, etc.". That's basically what the majority of fan work is, reproducing a work, or part of a work, by your own means; not simply taking it.
The former is a common problem that includes basic piracy and art theft. It's easy to define and enforce because you have literally (or almost literally) the same product in the hands of another person who doesn't own it and shouldn't decide what is done with it.
The latter is a much more complex issue, because you run into the problem of "how much is TOO much"? If I sing the music off-key, am I no longer in trouble?? Or am I in even more trouble, because I reproduced the original product in a way that makes it sound bad...? What if someone else sings with me, and they do harmony that wasn't present in the original? What if I change some of the words?? What if I change part of the melody??
You can make a legal case about any of these kinds of things, but it's a muddier concept simply because there are so many. And if you decide to make a blanket statement like "NO ONE is allowed to sing this song in any way except for our contracted performers" then you start hampering the circulation ability (and thus, popularity) of the art itself...which causes many to pedal back by varying degrees.