I graduated May 2017, so I've been paying off my loans. Also I'm over 24, and I took longer than 4 years. The school billed Fall 16/Spring 17 in 2016, but I paid for Spring in 2017. My tuition was paid with a mix of loans and grants.
On my 1098-T, boxes 1 & 2 are empty, but further down it breaks down the expenses to my loans, refunds (I got more moeny than I needed), and grants.
I called the school and they told me it was on me to report how much I paid. Considering my loans were automatically disbursed to the school, do I count that as tutition paid?
For example would I do Tuition-Refunds-Grants=Amount spent if it's all loans or do I simply report my grants?
Yes, you can consider tuition paid with loans as paid by you in the year that the school was paid. You paying off the loans isn't a factor, just when the tuition was paid. Your calculation does seem correct, if that was your situation, but make sure that the loan was paid to the school in 2017, and not late 2016.
When you are entering your 1098-T, Click the link What if this is not what I paid? and enter your actual payments there.
If what you paid with loan money is not enough to get you the full credit, there is a way to count expenses paid by grants.
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 $10,000 in box 5 of the 1098-T and $8000 in box 2. At first glance he/she has $2000 of taxable income and nobody can claim the American opportunity credit. But if she reports $6000 as income on her return, the parents ( or you if you claim yourself) can claim $4000 of qualified expenses on their return.