What do you think Kobe means? It specifically refers to a region of Japan. The breed of cattle is actually called "Wagu." If you want "kobe beef" that's fed and raised in a different manner, you can get Wagu and not pay the exorbitant prices.
'Kobe' is actually a city in that region of Japan, so the name already doesn't match the geographical location. Even pedantic-marketing Kobe beef doesn't ever have to visit Kobe.
