Actually not in this case, as Amazon doesn't provide cost of living adjustments. Location isn't factored into pay amount.
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.
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)
So for example, that seems about right for Portland, OR.
Additionally, you don't mention how many total years of experience you have which would also let people compare. Ex: 2 years of total experience (straight out of college) vs 2 years at amazon, and 10 years elsewhere.