TurboTax allows my child to take the American Opportunity tax credit when she entered that I will claim her as a dependent so may she take the tax credit or is it wrong?

I believe that she is not eligible to take the American Opportunity tax credit on her return because I am claiming her on my tax return, but Turbo Tax is allowing it.  I confirmed she entered that I will claim her.  Note that she is in her second year of college and we have never claimed this before and that our family income exceeds the limits for the tax credit.