There's a new urban myth among college students that says they can get a $1000 (or sometimes $2500) from the government just for filing a tax form. For most of them, they simply aren't eligible. A full time unmarried student, under age 24, even if you don't qualify as a dependent, 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. It is usually best if the parent claims that credit.
You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.
Reference: Line 7 instructions for form 8863. https://www.irs.gov/instructions/i8863