With all the federal education grants/aid/what have you, it's hard to imagine that your institution is purely jayhawker funded.
It's a damn shame that the internet has given terrible people the reach to make life even harder for educators, regardless of whether that's the specific concern here.
I suspect it's more a general anti-AI training thing, actually.
Nobody technical I ever worked with had an issue with putting the course syllabus up on a website before now.
I didn't mind if students recorded my lectures, but I did ask them not to share beyond the students as a courtesy to both myself and other students. I didn't want students being afraid to ask questions in class because they might be recorded. And I didn't want my lectures really going outside, especially if I gave advice or teaching tailored to the class itself. My technical experience is hard earned, and I'm not being paid anywhere nearly enough by a university for it to be shared to the public at large.
In this day and age, I'd probably take a much harder line. If I'm being paid to teach students, I'm not expecting the lecture to be fed into the AI maw. If AI wants my lectures, they can pay for it.