Do they have evidence for this or is it just based on hearsay?
I understand the bull is some sort of national symbol for spain or something like that? It won't be surprising that they would praise it so biasedly. Tigers vs bulls, usually tigers or lions should be able to take them down. It's the buffalo that the big cats might have problems with but i could be wrong.
Bull killing or injuring an elephant?
GTFO.
of course, in natural settings, a tiger can ambush a bull or a buffalo and kill it from behind or in stealth. in a gladiator pit or coliseum, it's daylight, one on one and no place to hide. no ambush, no stealth, no tricks. animal to animal, face to face, tiger will die, el toro bravo will kill.
spain was under roman rule for much of the early roman empire, and many spanish males joined the roman legions. it's no wonder that spain is a latin country, carrying much of latin culture and the language. when rome fell and was burnt to the ground, many roman colonies in spain withstood the test of time and wars. in segovia, the roman aqueduct is still intact. many roman fortresses are still intact today, such as toledo. it's better to tour spain if you are a roman history enthusiast than it is to tour italy. i lived in italy too.
it's legend, so much of the story is passed down by word of mouth or from generation to generation. but there are some writings on it, for example...
http://everything2.com/title/Bullfighting
"On the Culture Surrounding Bullfights
El Toro Bravo. The Brave Bull. The Spanish Fighting Bull. No animal is mightier, stronger, more dangerous, deadly, or majestic. El toro bravo is NOT an ordinary bull that many would associate with being a bull. It is a behemoth of creatures, and the much of the Spanish people believe whole heartedly that it is King of the beasts, not the lion. In ancient Roman coliseums, the strength and majesty of el toro bravo was tested by pitting it against lions, tigers, elephants, and bears; it won a vast majority of these matches. One of the many images the Catholic Church has for the devil/a demon is a giant bull, black in color, blood red eyes, fiery hooves, and immense horns. Because of the Catholic Church's influence in Spain, it becomes undoubtable where this image came from. El toro bravo has become a culture within a culture, a fanfare and spectacle within a fierce debate."
"Indeed, there are cave paintings in Spain that depict men lancing bulls and bison. The rituals of the corrida are Pagan in origin. El toro bravos 'slain' for sacrifices to the gods. The Roman Empire more than likely adopted their coloseums and gladiator matches from ancient Spanish corridas (although vice versa is not without probability as well). When the Roman Empire became Catholic, so did Spain, and thus ended the Pagan practices within the country. But the Pagan influence was not driven out completely; much of the Patron Saints of cities that have bullrings, or plaza de toros have pagan origins. The church has simply assimilated the pagan traditions and made it their own. Most fiestas occur around or on Catholic holidays (once Pagan celebrations), and usually these fiestas are crowned with one or several corridas. So the religious connection becomes obvious. The Catholic Church is traditional, ritualistic, and resistant to change; the matadors are traditional, ritualistic, and resistant to change. Catholic priests attend corridas, bless the bulls, matadors, swords, everything. And the matadors pray to the Patron Saints and to God for a good fight. In the permanent plazas del toros, there are churches located inside the arenas themselves."