There's some very important context missing:
The playlist in question was a collection of those videos of kids with creepy pedophile comments on them. She was ostensibly trying to help YouTube, but it's not surprising that YouTube would ask her to take it down -- the whole problem was that people were creating a sort of ad hoc pedophile ring through playlists and comments. A public playlist was basically a one-stop shop for those creeps, even if it was created with noble intentions.
I know some people here like to fantasize about YouTube being evil incarnate, but I'd say it was correctly erring on the side of caution here.