Why is MLB's final called "World Series"?

In 2010, Texas Rangers became the champion of the American League for the first time ever in the history. Colby Lewis' outstanding pitch, which allowed only three hits and one score from NY Yankees, in the sixth game was the best part in the league championship. Many Japanese baseball fans also watched the sixth game to watch how well Lewis would do against NY. Lewis became very famous in Japan after he had played in one of the Japanese Professional Baseball, JPB, teams, Hiroshima Toyo Carp, in 2008 and 2009th seasons. Then, in 2010, he came back to Texas, which selected him as 38th overall player in 1999 MLB Draft, and played an active role in this season, especially, in the postseason.

After seeing Lewis' pitch in the sixth game, many Japanese news papers put the articles about his pitch. "Our Lewis represented Japan!" Since he is not a Japanese, the title was really not correct, but what the news paper tries to say is that "the level of JPB has grown so much." Since the  beginning of 2009, naming the championship of MLP "World Series" has been a debate in Japan since 2006, when Japan got the champion in World Baseball Classic, WBC while the U.S. lost before advancing to the final tournament. JPB side has argued that MLB's champion and JBP's champion should go against each other in World Series to decide the real "World Champion."

I disagree with the JPB because it's obvious that the level of MLB is much higher than JPB's. Then, why did the U.S. fail to advance to the final tournament in 2006 and got the fourth place on 2009 while Japan got the championships in the both WBCs? There are many reasons that both Japanese and American journalists mention why the U.S. didn't do well in WBC: Because the U.S. teams didn't prepare enough for the games and many American MLB's star players refused to participate WBC. To me, these reasons almost sound excuse, but I have a clear reason why MLB's level is much higher than JPB's. It's because MLB does not limit the number of non American baseball players while JPB allows each teams to have only four non Japanese players. More than half of players in MLB are non Americans and many of them have become successful and star players, such as Pedro Martinez, a Dominican and Albert Pujols, a Dominican.

Today, many top players from Japan and other countries, such as Korea, Ruperto Rico, Cuba, and Dominican Republic, have joined in the MLB teams and worked hard to become successful in the highest baseball league MLB. Getting the championship in MLB means to become the champion among these top players in the world. Therefore, MLB's World Series  are meant to decide the real "World Champion." If Japan still wants to argue about the topic of World Series', JPB, at first, should welcome unlimited number of foreign players to play in Japan.