[benmathes]

Which is almost more arrogant, since it translates to "The country in the center". It's a little easier to understand why there's a strain of "we are the center of the world, outside our borders are barbarians" when you look at pre-modern borders: China is bordered by oceans, the russian steppes, the xinjian desert, and the tibetan plateau.

[cldr]

Well according to Wikipedia (yeah I know, but I don't feel like searching elsewhere) it may or may not be taken with the meaning "center of the world." And even if it is, it's more of an observation than a boast, since from their perspective they were in the middle of a bunch of other countries like you said. And hey, they call America "beautiful country" so they're not being stingy.