Maybe. Let's get this all straight. 529 distribution for $13,000 and tuition refund of $6,000. If those are the only numbers, then we are missing room and board, school supplies, etc.
A 529 distribution is not taxable when spent on qualified expenses. The extra $6,000 may have gone towards qualified expenses. If living at home, a good portion of it would still count for room and board. See page 52 for qualified distributions at IRS Publication 970, Tax Benefits for Education.
If you actually have taxable income and earnings, the program will calculate it after you take out everything. The name on the 529 can be the one to bear the brunt. The first$12,400 of income is not taxed so a student usually does best to claim 529 income that is in excess of expenditures.
However, you do not need to enter the 1099-Q at all if all of the distribution is not taxable.
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