The university gets some income from graduate labor. Grad students write papers about work their PI gets funding from the NSF/whoever for. PIs then write a new grant awarded based on their proposal and prior work. The university then takes some percentage of the grant off the top. How that compares to expenditures needed to pay for the education of PhD students by the school, I do not know.

But that does not differentiate between US and non-US students at all. The original argument was that non-US students generate more revenue for the schools.

There is a huge difference in how universities treat their Masters vs. PhD students. Indeed, universities are not making loads of money off international PhD students (most receive free tuition, a stipend, etc). However, international Masters students are cash cows for most universities (most pay full price -- or someone does for them).

I attended MIT for undergrad as well as master's. Most master's students I knew did not pay tuition (it was typically covered by their lab or through being a teaching assistant). On balance I wouldn't describe MIT master's students as "cash cows" for the university.