This is right: they and the rest of the FAANGs pay based on the local market.
On the other hand this means areas with lower costs of living but strong tech job markets can be a very good deal: Pittsburg is one people often bring up.
Boston isn't as cheap as Pittsburg, but it's far cheaper than the Bay Area with pay that's nearly as high. I'm very happy here.
The problem for the hypothetical KC Googler is that there are substantially no other high paying tech jobs in KC. There's Cerner, but they pay seniors ~1/3rd what Google pays (and it seems to get further from Google comp as you go up the ladder). So if you want to negotiate with Google to increase your pay, you have no credible best alternative to a negotiated agreement (BATNA). If you want to work for any other high paying tech company, you have to leave town. Google, knowing they are the best game in town, would face less upward pressure on wages.
I mean, as a matter of simple fact, Google does not pay the same in different metros. Nor do any other large companies I'm aware of. The pay is adjusted to what is required to attract talent in those metros.