Unlike other Shmula readers, I can't jump from this to the conclusion that Amazon are based on Six Sigma or Lean. Instead, what I hear Bezos saying is "We studied what's out there, and went our own way." And that way is a game changer in retail worldwide, worthy of study in its own right...It is interesting to see what Amazon continues to do. I think you are right that they have learned good things and are applying them their way. Often Bezos does what I see as much more fundamental lean thinking than those that spout the term a great deal.
For example: Bezos going to the gemba, Bezos root cause analysis ... Bezos understand the weakness of traditional accounting more than most any executive (he was a Wall Street analyst), this is way more important than I ever see mentioned in what makes him, and Amazon, different.
Bezos practices long term thinking better than nearly every "lean" company (though Toyota, and some others do this very well). From this mindset many things spring - focus on long term customer value, invest in value stream (Amazon's purchase of Kiva robots for example). Willingness to go against the current fashion, being directed by Wall Street analysts what is in the businesses, etc..
There are also job announcements, over the years, looking for lean experience and expertise I have seen from Amazon (which is a clue they are interested in lean).