The statement is - False.
The modern bullfighting has a long tradition, but it didn't originated in Mexico, instead, it originated on the other side of the Atlantic, in Spain. The bullfighting was first introduced in the year of 711, and it was organized in honor of the coronation of the King Alfonso VIII. It can be said that the bullfighting, or ''corrida de toros'' as it is in Spanish, has a connection, in the way of performing, to the Roman gladiators.
Since the Spanish managed to conquer lot of territory in the New World few centuries after this entertainment started, it got spread over a vast territory where the Spanish had their influence. Nowadays, it is practiced in Central America, South America, and part of the United States, and of course, in the motherland, Spain.