My understanding is that it's not really bookkeeping. The tuition is still paid, just by the federal government (or grant provider) to the university instead of by the student. The students can't afford to pay taxes on this, so presumably universities will have to increase stipends to cover the difference. Effectively, the government is increasing taxes on its own grants---which is a (politically) clever, backhand way of cutting research budgets.
I would note that it's also possible to get a tuition waiver from being funded by a non-external source, or from technically an external source that's functionally the same (A CA state agency paying a PhD student at UCSF, for example).
