Here’s what I have to say:

“A middle-class student from Pennsylvania can’t afford to take an unpaid internship in New York: it would cost him thousands of dollars just to live here for the summer, and he’d lose the opportunity to make a salary at a paying job.”

So he doesn’t take the job. He is not forced to go to New York to be an unpaid intern. if he can’t afford it, he doesn’t take it. The kid has the right to an opportunity for an internship, but a right is not a guarantee. He has no right to take whichever internship he wants at any price he chooses.
 
“Why is it right to penalize those less wealthy in an educational setting?”

No one is being penalized here. This is on par with saying that because I cannot afford to move to Alaska to take a job as an ice fisher, the ice fishing company is penalizing me. There is only a right to opportunity, you are not entitled to anything.

“Why can employers bypass the minimum wage and get free labor by using a special word that often serves only to indicate the unpaid status?”

Again, no one is forcing the interns to take this internship. There are ample opportunities for internships at other companies, many of which are certainly paid. If a person chooses an unpaid internship, they do just that—choose it. To accept an unpaid position and that complain that your salary is not high enough is ridiculous and irrational.

— 

“A right does not include the material implementation of that right by other men; it includes only the freedom to earn that implementation by one’s own effort.”

-from “Man’s Rights” by Ayn Rand in The Virtue of Selfishness