Q. Which approach is the correct one?
A. The return for the student , where TT treated the difference as income and identified her tax.
If you enter her details on the parent's return, TT only identifies that you don't qualify for the education credit and that one possible reason is that scholarships exceed educational expenses.
From Pub 970:
If and to the extent your scholarship or fellowship grant doesn't meet the requirements described earlier, it is taxable and must be included in gross income. You can use Worksheet 1-1 to figure the tax-free and taxable parts of your scholarship or fellowship grant.
https://www.irs.gov/pub/irs-pdf/p970.pdf (pages 5-7)
