It means something different over there. In the United States, “sorry” has a few widely used meanings.
(1) As a form of apology. I’m sorry I kicked your shin.
(2) As an expression of sympathy. I’m sorry for your loss.
(3) As an adjective meaning inadequate. You are a sorry specimen.
To these, the British add
(4) As an interjection meaning “I didn’t hear you, could you repeat that?”
A: “Lie nuff cacophany?”
A: “I said, would you like another cup of coffee?”
I’m terribly sorry but we’re just doing it to be polite. Much like Japan, when your country develops it’s sense of manners under a system where armed warriors are the norm (knights/samurai), you tend to establish patterns of speech designed to reduce aggression.
At this point the swords are more or less gone, but the speech patterns are traditional and cultural so we carry on carrying on.
Sorry if that doesn’t illuminate it for you.