Is it a problem if Buffalo wings are made outside Buffalo, New York? Do you expect Canadian bacon to be made in Saskatchewan? Should Manhattan clam chowder be made in Manhattan? Are french fries imported from France?
Probably not, unless they are claiming it's a product of Arkansas. Like your example above about Italian sausage, it's a categorization of style of food, not a product from a specific locale.
Yeah, there are things out there that are called "Philadelphia Cheesesteaks" that amuse and alarm people from Philadelphia, but no one has (sincerely) suggested outlawing them.
(I always thought "Greek" was a style of yogurt.)