Why am I protesting my property taxes?

I have a market value of $350k, but my appraised value is set at $220k. I filed a protest a few weeks ago, and suggested the market value be set to $290k which is more in line with other homes in my neighborhood. HCAD came back with a settlement offer of $325k market value, keeping my appraised value at $220k. But their email said that by law they have to go with the lower of the two values. My question is that if they have to go with the lower of the two values, why are we arguing about the market value being 345 or 290 or whatever? Won't they just tax me on the $220?