This isn't really relevant because of the counter-notification provision, right?

If the material wasn't infringing, the students could counter-notify which would allow their ISP to be protected and keep their site up.

Counter-notification is certainly a possible next step. But it's a reactive step.
And you have to do it under penalty of perjury. It's more complicated than it might seem at first glance.
Even so, I strongly suspect it'll happen.
But it seems like it hasn't been done yet.