This is a good principle to maintain, I think.
I'm not a professor, but I manage a team of about a dozen people. The maxim I have is: "You're responsible for anything that hits git."
Don't care if the LLM generated it, or the LLM told you if it's a good idea. If you commit it, you are endorsing it as a good idea - so you're the one I'm going to ask about it. I see the same principle at work in your pedagogy.
> I'm not anti-AI (and really, what could I do if I were?) since I use it myself, I'm just anti-slop, especially from my students.
This hits. Especially this part:
> and really, what could I do if I were?
My completely unsolicited opinion: you're doing a responsible thing by teaching these students how to use AI as a reference, and keeping them honest about not using it as a substitute for their own critical thinking.