Not true. If it were based on cost of living, then Google would pay more for you to work from Hawaii than from Alabama. (Spoilers: it doesn't, they're both in the same salary band.)

It's slightly more true that it's based on the local cost of labor, but even more so that it's just based on the state, with carveouts for MSAs (which are defined based on county) surrounding certain offices commanding higher salaries.

You'd make just as much working remotely in Matamoras, PA as you would working out of the NYC office in Manhattan.