Yes, based on the numbers you provided, she has $15,000 of taxable scholarship income. You should be be able to reduce a little by entering the cost of books and other required materials including computers (but not room & board). There is a place for this, in the interview. There is no additional tax form. You use the 1098-T and your own financial records. Your are further correct that form 8615 does come into play.
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There is a tax “loophole” available. The student reports all his scholarship, up to the amount needed to claim the American opportunity credit, as income on his return. That way, the parents (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship. You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses.
Using your numbers as an example: Student has $55,000 in box 5 of the 1098-T and $40,000 in box 1. At first glance he/she has $15,000 of taxable income and nobody can claim the American opportunity credit. But if she reports $19,000 as income on her return, the parents can claim $4000 of qualified expenses on their return.
