Another issue: scholarships that pay for tuition, fees and course materials (QEE - qualified educational expenses) are tax free. Scholarship money that pays for living expenses (e.g. room & board), whether on campus or off, is taxable income to the student. So, if your "full scholarship" also pays for room and board (R&B), that portion of of your scholarship is not tax free. As such, a 529 distribution, for R&B, up to the "allowance for attendance" amount, is tax and penalty free, since it was not paid for by "tax free" scholarship.
Back to your original question, anyway you structure it will qualify. You mortgage interest, as well as utilities, insurance and real estate tax, would count. Rent paid to your parents would count. Just living in a home owned by them would count.
"Rent" or shared expenses, paid by room mates, would reduce the amount your could claim. But, that's mostly academic, as your net amount is still likely to be more that the school's "allowance".
