It will be taxed in both situations, but are you saying that the 10% penalty is applied after the 1098-T is entered? When you say the tuition was "paid in full" by the distribution, was it even? Distributions plus scholarships equal tuition and fees?
For example, if tuition was 10,000 and distributions were 10,000, and you take 4,000 for the credit, you should be taxed on the earnings of 4,000.
If tuition was 10,000 and a scholarship on Box 5 was 2,000, and the distribution was 10,000, and you take 4,ooo for a credit, you will be taxed on 6,000 and penalized on 2,000 because there was only 8,000 of tuition after the scholarship applied.
Same example, but you allocate the 2,000 scholarship to Room and Board, the student will need to claim the 2,000 as income and you are taxed on 4,000 and no penalty.
If you tell us all the numbers, (the 1098-T and 1099-Q) we can give a better answer. The American Opportunity Tax Credit needs 4,000 for the full credit. if the distributions plus scholarships are more than 4,000 above the education expenses (tuition and books) there will be a penalty. But the tax, including the penalty, should be less than the credit if you clicked "Maximize my Credit" in the education section.
