There's two separate issues on support.
Where TurboTax (TT) specifically asks if the filer supported themselves with *earned income*, it's seeing if he qualifies for the refundable portion of the American Opportunity (Tuition) Credit*
For whether he can be claimed as a dependent supporting yourself means paying for more than half your living expenses with any money of your own, including savings, student loans (but not scholarships), and income from any sources, including unemployment.
In your family's case, it's a triple whammy. He doesn't qualify as your dependent because he supports himself. You don't qualify for the tuition credit because the student is not your dependent. He doesn't qualify for the refundable portion of the credit because he is under 24 and does not support himself with earned income. The good news is that the non-refundable portion of the tuition credit should lower his tax liability to zero.
*A full time unmarried student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. You usually must have actually paid tuition, not had it paid by scholarships & grants. It is usually best if the parent claims that credit.
