Is it a $50 fee EACH charge, or for the year? That may be a deciding factor.
As long as your parents pay it off, I wouldn't see a thing wrong with it.
I would notify Chase before making the purchase the first time if it's several thousand, just so it doesn't get declined.
I'm sure it's not unheard of for a student to have a hefty savings account to be able to pay for college w/o any income. IMO it's a far more reasonable (explainable) charge than someone spending $100k at American Express Gifts in a year and only bringing home $60k income and I'm confident that happens here all the time.