Apparently it's only going Mach 7 or so by the time you're down to 200K feet. Doesn't matter. It would have to be a lot slower than that and it isn't. You're a meteor, and the thickest part of the atmosphere is still below. When those tiles are gone from around you, you're going to burn.
Looks like I was right the first time and it's more like Mach 15 at 200K feet, which is also just about the maximum re-entry stress on the spacecraft. Different numbers were flying around in the first hours after the tragedy.