I fail to see the problem with this. Especially when it's products made from animals that eat the grass around that place. Or anything soil-dependant really. Wine is very different depending on where it comes from.
It's easy to poke fun, but DOP isn't just about region and it does matter, at least for many things.
I don't know that "you can't call it X" is the right approach, but there should be some really clear to consumers way of saying "X was made to a particular standard" vs "all bets are off with Y" - then let them decide.
Well in South Africa we have a sausage called boerewors. My understanding is that you can only label it boerewors if it has certain specific percentages of certain specific fillings. Anyone can make boerewors and call it boerewors, as long as they stick to those ingredients and percentages.
Things that fall out of those ranges are simply called wors. Similar to the difference between a pork sausage and a pork banger.