It's for the same reason that all sparkling wine is in America is called 'champagne'. We don't participate in PDO / PGI / DOP / etc. agreements with most foreign countries. We do have requirements for specifically American-made items to have similar tules, such as Bourbon (so Jack Daniels is Tennessee Whiskey, not Bourbon). But just as America doesn't recognize the European protection for parmesean, champagne, etc, European countries don't recognize the American protections.
I've talked to a local Wagyu farmer, and he said that true Kobe has to be processed in Japan (and he said it in an ambigous enough way suggesting that it might be possible for American-raised cattle to be shipped back to Japan for processing), and they're given a specific diet and treatment that doesn't happen in the US. (I also tried to talk him into selling me 1/2 a cow, and at the time (3-4 years ago?) he said it was in such high demand that all of his cows were sold before he even started raising them. At that time, Wagyu was still pretty rare in the US, and it was being sold as Wagyu ... it only seems to be more recently (last 1-2 years) that I've people selling it in the US as 'Kobe'.
Most of the "American Wagyu" has also been cross-bred with an American cattle. (The story I've heard is that the sperm was brought over, not live cattle, so they had to start with American heffers). So it's going to have some percentage of Longhorn or Angus in it.