I think this depends. Universities seem to have the power to generate "tuition waivers" that accompany TA positions and a few external fellowships such as NSF G

I think this depends. Universities seem to have the power to generate "tuition waivers" that accompany TA positions and a few external fellowships such as NSF GRFP, but if you're funded solely from one or more of your advisor's grants, I believe that, at most places, the grants are actually used to fund the full cost of tuition. And as we all know, tuition is kind of insane at most places due to bloated admin. Source: what I remember my advisor telling me when I was a grad student