Take a look at MIT's response to the administration regarding the University Compact (https://en.wikipedia.org/wiki/Compact_for_Academic_Excellenc...). You can see that MIT has an excellent understanding on how to reply. AFAICT the administration did not reply furiously (if I missed their reply, I woudl appreciate a link to it).
I can also predict the next step here: UT Austin is likely to agree to the compact and will be given a huge monetary award (although I don't think it's a foregone conclusion- they didn't reply within the deadline which suggests that they are working behind the scenes on an agreement).
I have—fortunately—very little personal experience with being extorted by corrupt officials, but I'd wager another facet is to try to ensure all communication is public and recorded.
This forces them to cloak their real demands in something deniable, and that means you can play naive and act like the subtext was never seen.
I can also predict the next step here: UT Austin is likely to agree to the compact and will be given a huge monetary award (although I don't think it's a foregone conclusion- they didn't reply within the deadline which suggests that they are working behind the scenes on an agreement).