It seems that the difference between payments and scholarships is what is being used as the tuition we paid. However we paid the "payments" in box 1. If box 1 was total tuition and that was reduced by scholarships, that would make sense. But, payments clearly equals what was paid, not tuition.
At tax time, "payments" are irrelevant. What matters is what are you qualified expenses. TurboTax assumes (and rightfully so) that the difference between box 5 and box 1 is the net tuition expense not covered by (allocated to) scholarship.
If the scholarship was not restricted to being used for tuition, you have the option of re-allocating it to other expenses (primarily room & board [R&B]), to free up more tuition for the credit.
But, it only takes $4000 of net tuition to claim the maximum amount of the American Opportunity Credit (AOC). And you have that much already, so there should not be any concern. R&B are not qualified expenses for the AOC or the other credit or tax free scholarship.
" If box 1 was total tuition"
Box 1 is almost always total tuition & fees, and nothing else. Anything else is a mistake on the school's part. It's more likely you are misunderstanding the 1098-T.