That's some bizarre logic. Tax-free day doesn't "give back" anything, it just slows down the rate at which they exceed what they thought was acceptable.
You're both right. There's a tax-free day to slow down the amount of tax brought in, but state law does require returning unexpected tax windfalls that exceed inflation and population growth. Wikipedia has a good overview: https://en.wikipedia.org/wiki/Taxpayer_Bill_of_Rights
