So another way of making my point is that the task of generating signals for employers at a no-name college is pretty much comparable to the task at a top-tier university. You get brighter students because of the sorting function of admissions, but the task is really the same and anyone competent in the field can do the work of generating those signals for employers at any of those schools.
Given that point about the job of generating signals to hand to employers on a piece of paper called a transcript alone, you wouldn't expect to see a strong correlation between quality of professor and quality of undergrad. And yet we do see this correlation. That can't really be explained by the signalling theory but it's an important element of the world of higher education.