Education

Yes, it is true that the student can claim scholarship as income in order for the person claiming the student to claim an education credit. 

Not so much a tax "loophole" as the IRS encourages Taxpayers with education expenses to file in a way that results in the best tax advantage as possible. IRS PUB 970 has some great examples of how to do that. The problem is there are SO MANY ways expenses and payments can be allocated, it can be very confusing. 

IRS PUB 970

If Box 1 (what was paid to the school) in the amount of 6330.69 was covered by a scholarship which HAD TO BE USED for tuition, that expense cannot be used towards an education credit. 

The student can only claim "unrestricted" scholarship amounts. 

It is a bit unclear when you say  "The amount in box 1 from the 1098-T is the amount of tuition for the school but it's also the amount of a school scholarship awarded to her that could only be used to tuition at the school (basically a 1 year full tuition scholarship from the school)." I think this means the amount of tuition and the amount of the scholarship each were 6330.69.

Then I understand that the 5039.31 is the scholarship not used for tuition. 

And there are 1900 additional expenses. 

If I understand your numbers, the student would only have 1900 in expenses (for you to use towards a credit) even if she claims all the excess scholarship. (5039.31)

It COULD be advantageous for the student to claim the income for you to get a credit, but keep in mind:

the American Opportunity Tax Credit (AOTC) is worth the most, (compared to the Lifetime Learning Credit

is "refundable"

Maxes out at 4,000 expenses

and CAN ONLY BE USED 4 TIMES per student. 

If the student might have 5 calendar years of expenses to earn a 4 year degree, you may want to save the AOTC for next year. 

If you can get the same tax advantage with the 1,900 expenses using the Lifetime Learning Credit, don't waste the expenses on the AOTC. 

If the tax the student needs to pay is more than the credit, don't have the student claim the income. 

You can enter the 1098-T and go through the education interview in your TurboTax program. 

The section is lengthy and you need to go through to the end where you will see  "MAXIMIZE MY TAX BREAK".

When you click this, the program will tell you the best way to report the expenses and income to get the best tax break. 

YOUR TurboTax will tell YOU what the student needs to claim as income. 

Scholarship income is reported on line 1 of the student's 1040. 

YOUR TurboTax program does not know things like, what the impact will be on the student's tax liability or how many more years the student will have expenses.