Why Can't the Americans?

Why is it that seemingly every British actor can do an American accent that sounds completely authentic to my American ears, yet almost no American actors can do British accents that sound authentic to me?

It can only be due to the superiority of American dialect coaches...right?

And on a quasi-related note: Remember how Sid Caesar used to ad-lib in other languages, and it sounded like he was really speaking the language, even though it was just gibberish? I've always wondered what it would sound like if someone did that to "English".