I want to say, up front, that there are a number of private colleges that are notorious for claiming that students who dropped out signed up for additional classes that they did not pay for. There have been a number of media articles about that problem. You may want to run some Google searches for your college's practices to see what comes up.

Unpaid tuition debt is one thing. Student loans are another thing, entirely. If you assume that paying a claim by your school for unpaid tuition will cause a Sallie Mae student loan to be paid off, no, that won't happen.