This is what I was told, but others ITT seem to have heard differently. In the examples that you know of, was the person relocating to Seattle or somewhere else, like SF?

It may be that what I was told was correct, but they were referring only to Seattle and not places like SF where cost of living is very high.

A college friend and I both got hired to Amazon in the same round of campus hires. We both accepted Seattle positions, but then between accepting the position and graduating, his team moved to SF, and his offer got increased to compensate for the higher COL there.

Two other situations involved coworkers transferring teams from Seattle, one to Toronto and one to India, both had COL adjustments to their salary.

(Admittedly the evidence is less strong in the latter two cases because they involved simultaneous country changes)