Anecdotally, in the last recession the difference in starting wages between an MIT alum and a state school alum were nearly 3x. When company hiring gets tight the brand name degree makes a big difference.
I sort of doubt that will make enough of a difference in this case. If they plan to go to MIT or similar for grad school, they might as well take the free undergrad. The opportunity cost of spending $100k vs free is pretty big in my view when the horizon to the graduate degree is short.