The thing with copyrighted content, though, is that even if the file you're checking might be infringing on copyrights in certain cases, in other cases it might as well be completely legit. I wrote about this on some earlier MU submission[1], so I won't repeat all that here, but all in all, even if you knew that file X existed on Mega's servers, it would be pretty damn haphazard to just outright delete it, because you might be hurting many legitimate users by doing so.
Anyway, I think Mega could secure user's files simply by encrypting the locator keys they have with the user's own key, and this data only gets decrypted and parsed client-side when the user uses Mega with the user's own key. This way you could only prove that a file exists on Mega's servers, but had no way to check which user(s) it belongs to without cracking the individual user data one by one. And of course, if you don't have any exact files to check against Mega, then you wouldn't be able to even figure out whether "content X" is hosted there somewhere, and neither could Mega (since they'd naturally only store locator hashes and encrypted data itself).
True, and it seems that Mega's copyright infringement reporting page[1] has an option for that:
Takedown Type: Remove all underlying file(s) of the supplied URL(s) - there is no user who is permitted to store this under any circumstance worldwide
They wouldn't really want that, would they? So as clever as it is, I doubt they do it this way.