I guess it depends who's made it private. It would have to be the plagiarist wouldn't it? Wouldn't YouTube just remove it if they had an issue with it? They wouldn't make it private, would they? (They might; I'm less than up with how things work as it's not a site I visit regularly, but it seems doubtful).
In which case, it's probably been done so that the masses can't read the comments pointing out that it's a plagiarised work. Then the plagiarist can safely invite who they like to view it, remove the comments, and claim it as their own in complete safety.
But, at least, as you say, Sas, it cuts down the number of viewers. Which is small consolation, but something, I guess.
LabRat