If you do not qualify as their dependent, then you can claim the tuition credit, on your return, even if they were the ones who paid the tuition.
Be advised that the American Opportunity Credit (AOC or AOTC) can only be claimed 4 times on a student. Since graduation year is usually the 5th year of college, it's likely your parents already claimed it the 4 times. The less generous Lifetime Learning Credit (LLC) is available.
