It is interesting to understand what the "bow" means. The one who bows the lowest (e.g. Obama) is the least of the two when it comes to respected/status. A good example is if an 19 year old female were to meet the President of Toyota in Japan she would bow deep about like Obama and the President of Toyota would bow just a little. It is not unusual that when two Japan businessmen meet for them to trade business cards with the description of their positions printied on the back. That gives an indication as to how deep each should bow.
It is a disgrace that our President bowed so deep which indicated that the other person had more respect/status than our President.