Q. Are 1098-T Box 1 monies considered paid by the graduate student, and thus eligible for deductions, if they are part of the student's compensation?
A. Yes, if it was taxable compensation. So, it somewhat depends on how the compensation was reported, W-2, 1099_MISC, 1099-NEC. box 5 of the 1098-T. More info is needed for a definitive answer.
Typically, the way it works is the compensation is reported on box 5 of the 1098-T, as scholarship and not compensation. Unless the conditions of the grant say otherwise, the student is free to report some of the scholarship (box 5) as taxable income, so he can claim some of the tuition (box 1) for the tuition credit.