First Obama, the President of the United States of America, which at one point was a sovereign country, bowed down to the Saudi King. There was a bit of outrage, but his "people" explained, "of course he didn't bow. The King was just a much smaller man." Also, "It's really hard to tell what he was doing. That other guy obscurs him."
Well, now he's bowed to the emperor of Japan.
Here's the thing. American presidents don't bow. They shake hands as equals. If he wanted to pay his respects to this much older man, he'd have bowed his head, not bent over so far you could iron a shirt on ihs back!