If they are seriously concerned about the debt of MIT undergrad I don't think suggesting they go into further debt on a risky venture like a startup while still an undergrad is brilliant advice.
Taking on personal debt is by no means a required part of starting a startup in the US, and one of the points people have been implicitly making is that the connections you can make, the entrepreneurial activities at, in and around MIT will make taking on debt even less necessary.
Although this is not the OP's planned career path, he's planning on a startup after getting a Ph.D. and working a normal job for a while, which will also allow him to pay down the debt incurred in getting his undergraduate degree before the startup.
Another detail about MIT not yet mentioned: professors are formally allowed to work one day a week on things like their own startups. So "making a connection with a professor" includes the possibility of getting paid to work at such a startup which of course can be very educational about startups. And also get a different type of recommendation from "a MIT professor" that could also be useful in getting into a grad school.
Although this is not the OP's planned career path, he's planning on a startup after getting a Ph.D. and working a normal job for a while, which will also allow him to pay down the debt incurred in getting his undergraduate degree before the startup.
Another detail about MIT not yet mentioned: professors are formally allowed to work one day a week on things like their own startups. So "making a connection with a professor" includes the possibility of getting paid to work at such a startup which of course can be very educational about startups. And also get a different type of recommendation from "a MIT professor" that could also be useful in getting into a grad school.