The IRS makes no effort to match the numbers on the copy of 1098-T they receive from the college to the numbers reported by the taxpayers on their tax return. The only match is to whether a 1098-T was actually issued.
The numbers, you enter in TT are "crunched" by TT and usually do not actually appear anywhere on the IRS forms you submit.
Your fixation on the 1098-T being a controlling document (it isn't) is keeping you from understanding what you're being told:
1. You're allowed to claim the AOTC even though your student dependent is on full scholarship.
2. Your student has to report his excess scholarship as income.
3. Reporting even more of the scholarship as income is what allows you to claim the AOTC.
4. Getting TT to do all that correctly can be difficult and short cuts are recommended.
