Kobe is a district in Japan and you are right it is not from there. Wagyu is the strain, it is higher in fat content and is the strain that is being raised in the American west, it is sold as American Kobe. Much of it is shipped to Japan. Brisket is not a cut that the japanese are interested in so it does sale, in the West atleast, at a good price.
The reason Kobe beef is fed beer is to increase appetite and they message the animal because of the lack of free range.
Snake River Farms and Kobe of America both produce Wagyu beef and both use Kobe references because that is what Americans have heard of.