The user's javascript that encrypted the file can also make a hash send it to mega, and then they check if they already have that.
EDIT: They never get to see your key or what is in the file.
EDIT: They never get to see your key or what is in the file.
[1] http://en.wikipedia.org/wiki/Known-plaintext_attack#Present_...
Of course this will only give you the key to that one particular file, not any other files that you do not have yourself.
Assuming that it works this way, it would allow Mega to figure out if you own a known "bad" file. Just take something like "New_Jay-Z_Album.zip," hash it, and try the hash against your encrypted files. It seems like Kim is trying to avoid this problem.