This is no different than if Apple workers from China start selling iPhones in the US that is actually branded Apple iPhone, completely different from a "real" iPhone or exact copy, same thing. If anything the hundreds of years old "brands" should be more protected, not less so.
Calling something made in the US Champagne is the same as printing Made in Champagne, France on the bottle. If European businesses started making big bucks on products pretending to be Native American people would go berserk.