The problem with that theory is in the Asian culture, they don't expect any one outside of their culture to bow as it a very unique and respected custom with prescribed parameters.
You only bow from the waist to someone of higher rank or standing than yourself, which means Obama has considered himself to be lower in rank than all the Presidents and Prime Ministers he has met.
A simple nod of the head is all that is required between people of equal standing.
Although, with the Chinese President, I'm surprised he did not kiss his feet.
(Edited because I left out a word.)