This simply isn't true.
During the Vietnam War, some American prisoners of war refused to bow to their North Vietnamese captors. In Asian cultures, bowing was not seen as a sign of submission, but rather one of respect. (Keep in mind that service members in captivity are required to
render basic military courtesy and respect towards their captors). American serviceman suffered terrible beatings at the hands of the NVA for refusing to bow. In response, Admiral Jim Stockdale, the senior ranking officer in the Vietnamese POW camp, insisted that American POWs simply not bow in public, so as not to provide propaganda for Western audiences, who would interpret the bow as a sign of submission.
It's not a sign of weakness, it's a sign of respect. Even Richard Nixon bowed to Emperor Hirohito.
UPDATE: I have received exclusive video of what people think that President Obama's capitulation in front of Emperor Akihito must have looked like.
KNEEL BEFORE ZOD!
($10 says that Jon Stewart shows the exact same clip tonight)