financial aid as income

Simple answer: TurboTax (TT) has it correct, you son has (at least) $5793  of taxable scholarship income to report.  Yes, the taxable amount is, usually, simply the box 5 amount (on the 1098-T) minus the box 1 amount. 

You get 0 qualified expenses, for the tuition credit,  because you paid 0 (room and board are not qualified expenses, except for a 529 plan distribution).  

 But, 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 an example: Student has $10,261 in box 5 of the 1098-T and $4468 in box 1. At first glance he/she has $5793 of taxable income and nobody can claim the American opportunity credit. But if he reports $9793 as income on his return, the parents can claim $4000 of qualified expenses on their return*.

You have another issue: "He took 0 class at last quarter since he finished all the requested credits".  To qualify for the more generous American Opportunity Credit (AOC), you student must have been considered half time or more.  You are good, on this point, if box 8 on the 1098-T is checked. 

Another possible issue: you may have already claimed the AOC the maximum 4 times, and will be limited to the lesser credit or deduction. To claim the most Lifetime Learning Credit,  you should increase his taxable scholarship by $4468, rather than $4000.  The Tuition and Fees deduction has a $2000 or $4000 cap, depending on your AGI.

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*You essentially have to use a work around in TurboTax (TT). Here's how I would do it. Enter the 1098-T, on your return, but only enter $4000 in box 1. No other numbers. You only enter the 1098-T to get TurboTax to check the proper box on form 8863. Lying to TurboTax to get it to do what you want does not constitute lying to the IRS.

Enter the 1098-T, exactly as received, on the student's return. In his interview, you should eventually reach a screen called "Amount used to calculate education deduction or credit" Be sure the amount in that box is $4000. That will put all his excess scholarship as income on his return.  

Be advised some people are saying they're not getting the "Amount used to claim the tuition deduction or credit" screen on the dependent’s . The alternate workaround is  to enter $4000 less than the actual box 1  amount, when you enter the 1098-T on the student's return or $4000 more in the box 5 amount.