TurboTax is doing it correctly.
While technically there is a provision that allows you to claim a tuition credit, from a practical matter it seldom works out. A student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit if he/she supports himself by working . You cannot be supporting herself on student loans & grants and 529 plans and parental support. It is usually best if the parent claims that credit.
If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable).
I assume the reason you're considering this is that your parent's aren't eligible for the AOTC, due to income. This only works out for the family if you have a tax liability of more than $500 to offset with the credit.
