They may be grounds for firing, but doing so could cause one heck of a mess. Campus protests, boycotts, etc.
The best deal would be to throw her a lot of $$$ to go away quietly. But she doesn’t seem to be the type to do that.
In fact, I’m also betting that there are other instances of her engaging in this sort of behavior out there. Probably already found and documented/screen-capped. This is the sort of classic drip, drip, drip scenario that scares the hell out of PR crisis managers.
“separate bonus” s/b “separation bonus” (or award).