Probably, the rule in most places is that minors can't make contracts, unless the contract is over necessities such as food or shelter. $300 isn't much to worry about though, to prevent future problems I would probably just pay it and move on.
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Yes, this fee can be collected from you by regular collection processes, reported on your credit report, and can even cause you to be ineligible for future student financial aid. I know of cases where this kind of debt caused administrative embargo (freezing -- no report) of college transcripts and the consequences of that are vast. Not worth it. College debt is not the kind of debt to get stubborn and self-help about.
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