can I add the one more thing?

If at the higher income, the parents do not benefit from a tuition credit AND income beyond the $500 other dependent credit, or just partial phaseout credit, and the dependent student can benefit claiming the tuition credit, it can be claimed on the student's return.  Parents relinquish claim, though student is not and does not file as independent.  Do the comparison, if the ODC is less for the parents than what the reduction in tax is for the student.

😳  Okay, this was for hypothetical purposes.  Just saw the OP said student has no tax to pay.  Nevermind.