Other way around. It's not that tuition grants are being treated specially if they're taxed. All grants and material benefits of this nature are considered taxable by the IRS. Graduate tuition happens to have been given a special exemption from being taxable, and this bill is aimed at eliminating that special exemption, treating it like all other grants and material employment benefits.
> Or tax the universites, not the students.
There are two problems with this. First, the incidence of the tax (who actually ends up paying) is completely unrelated to who the IRS collects the tax from. This is why, even though employers are required to pay half of taxes for Social Security and Medicare, employees are the ones who bear the tax burden: 95% of any increases in FICA taxes are paid for by employees (via adjustments to wages and salaries), and vice versa.