The school was wrong to issue a 1099-NEC for the stipend. It should have been reported as either Scholarship (box 5 of the 1098-T) or wages on a W-2.
Students that work for their school are exempt from FICA (social security and Medicare) tax. In my opinion, you are correct to report it as SCH income on line 1 of for 1040 (line 8r of Schedule 1, starting with 2022 returns).
That said, your student may get a notice from the IRS as The IRS considers anything on a form 1099-NEC to be self employment income. If that happens, you should reply to them with essentially the same explanation you used in this thread (except no, the IRS does not expect that some students will receive a1099-NEC for this income ).
