The other thing to keep in mind is many (most?) schools are putting the wrong amount in Box 1.  They had a hissy fit a few years back when IRS told them they could not use Box 2.  So they they have been throwing EVERYTHING paid in Box 1, claiming they don't know how much of the payments received were for tuition (a qualifying expense of the tax credit) and how much was for room and board (not a qualifying expense for the tax credit but a qualifying expense for the Q form).  

If you know for certain more than $4000 was paid for tuition and there is NO Q form, you are good to go for the credit.  But if there is a Q form, you really need to get those amounts correct, and get them in the right bucket.  Have the student print out their student account transactions to get the correct amount paid for Box 1.  The remaining amounts paid on the student account (room and board, etc.) can be used to properly determine taxes on the Q, if any.  In the OP, the Q amount and the qualifying expenses were close.  But if the qualifying expenses far exceed the Q amounts, there may not be any tax.