Q. Would I be able to claim the American Opportunity Tax Credit (AOTC) even though my employer covered the amount in taxes by doing a tuition gross-up?
A. Yes. That entire $13,000 is your taxable income. As such, you effectively paid your tuition, not your employer.
You say the employer paid $9000 for tuition and books and added the whole $9000 (plus a tax allowance) to your income. The IRS allows employers to give their employees up to $5250 of reimbursement tax free, if they set up a qualified plan. You should verify that the first $5250 wasn't tax free. If it was, then you can only count $3750 (9000 - 5250 = 3750) for the AOTC.
