They have an interest in protecting their own use.
They have a much less compelling interest in preventing the use of factual representations underlying someone else's use, let alone quashing their free speech rights.
Case law favors those who use TM as a shield, to protect their own marks. Case law is not so favorable to those who seek to use a mark to limit speech, rather than protect their own brand.
You cannot copyright a fact, for instance. You can't copyright the number 44 for the purpose of taking it out of commerce. You can't copyright ideas. Because people may need to use those facts for purposes of further study, social or other types of commentary, or just as fair use, to describe something that happened in the news, or to a pubic figure.
Now, of course copyrights and trademarks are not the same thing, but I'm trying to make a point with the comparison. As someone who has litigated numerous trademark disputes, in state and federal court, as well as before the USPTO Trademark Trials & Appeals Board, including against 2 national sporting goods companies, this "shield vs. sword" distinction is important, just from an equity perspective. What is fair?
Bond Schoeneck doesn't give a shtt about that because they don't make any money being reasonable, or actually following the spirit of the law. They have a client at SU in their marketing department who is cowed by McGuire's 25 years representing SU, while the marketing person probably hasn't been an SU employee (certainly not one making branding decisions for the University) for maybe a quarter of that time. The lawyer becomes the expert, and the client does what they are told.
This is how these things make the news, generating bad press for the university.