from the cited Stanford link
1) Parody
A parody is a work that ridicules another, usually well-known work, by imitating it in a comic way. Judges understand that, by its nature, parody demands some taking from the original work being parodied. Unlike other forms of fair use, a fairly extensive use of the original work is permitted in a parody in order to conjure up the original.
Just as I thought, "by imitating" is the keyword here. Not by copying it and writing comments. Else I could provide access to any movie for free. All I have to do is write a funny comment about it.
2) A commentary allows reproducing only a portion
That's my understanding, not pretending to be a lawyer
Still not sure a University would love to get involved, their reputation is their number one asset.
I know someone personally who got fire for self-plagiarism, writing something that was written by him before, but not quoting himself. The uni lost overheads of a fat NIH grant, but thought it was worth it.