There is a tax “loop hole” available. The student reports all his scholarship, up to the amount needed to claim the American Opportunity Credit (AOC), 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 example: Student has $51,484 in box 5 of the 1098-T and $48,070 in box 1. At first glance he/she has $3414 of taxable income and nobody can claim the American opportunity credit. But if she reports $7414 as income on her return, the parents can claim $4000 of qualified expenses on their return.
Books and computers are also qualifying expenses for the AOC. So, extending the example, the student had another $1900 in expenses for those course materials, paid out of pocket, she would only need to report $5514 of taxable scholarship income, instead of $7414.
