Andy, I was offered an (unpaid) internship at ML about two years ago. The hiring manager told me that it is ML policy not to pay interns. And my buddy who did a UBS internship said the same thing.
As far as unpaid internships go, they're a great way to build your resume. I had two unpaid internships during undergrad, and two paid during grad. The thing is, MOST internships are unpaid - the people who land the paid ones have better resumes/more talent. Meaning, the paid internships generally go to people who have already gained some work exp.
One thing to consider in the workforce is that most recent grads who land a job think, "Omg, they're paying me $60k because I'm worth it! Blah, blah blah. I'll get a raise and promotion in no time!" When, in reality, you won't be worth the $60k for quite some time. You need to learn their business, best practices, etc. This isn't true for people transitioning with a relevant skill set. But, for recent grads, it's pretty true.