saving for future repeated use because it always comes up:
People outside of America assume it is pure arrogance or some bigoted belief in American superiority that leads Americans to refer champions of American sports leagues as World Champions. The truth is alot more innocent. At least when it comes to Baseball.
But basically it's a tradition that dates back 50 years before the US was a major super power. In the early 20th century, the owner of the White Stockings wanted to name the championship series between the National League and the American League "the Championship of the World" because he believed that Baseball would spread to the United Kingdom, Australia, and then the world. He also wanted a more "grandiose" and "sensational" name that the newspapers could get excited about. It was basically a publicity stunt.
So, it's my contention that the belief it is a mix of naive ignorance and a public relations stunt that caused Baseball champs are referred to as "World Champs". Not arrogance. It's my belief that the other sports adopted this practice from baseball.
On strict logical terms, you are correct, but its a cultural tradition, a viral meme if you will, so I doubt it can be changed by an act of Congress or a Presidential order. Perhaps as Americans gain a more "international" outlook things will change.
http://roadsidephotos.sabr.org/baseball/name.htm