60% of the American Opportunity Credit (AOC) is non refundable. That is, it can only offset an actual tax liability.
You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.
Grad students are not eligible.
If you are eligible, you have answered something wrong, in the interview. But, a lot of people are just not eligible. See https://www.irs.gov/Individuals/AOTC