I’ve spent a lot of time in Japan and never bowed to anyone.
I shook hands and smiled.
Did anyone bow to YOU, and you didn’t return the sign of mutual respect though? Customs may change for business people and the like over time, but when it comes to protocol for Heads of State it is a bit different.
I've lived there, twice for a total of 40 months as a Marine Corps officer. I've bowed plenty of times to Japanese dignitaries, their wives, JSF Officers and others in more formal, ceremonial settings. And certainly, this is what the military or DOS protocol would demand - nothing wrong or submissive about it.