There is a thriving craft cheese scene. I'll walk down to my local farmers market here in Northern Italy later and there are a handful of stalls selling various cheeses. If that isn't happening wherever you live, it's not bacause of the rules about Parmeggiano labeling.
Perhaps I'll also pick up a bottle of one if the "metodo classico" bubblies since the Champagne is way over priced. There is a nice wine-by-the-litre place on the way back.
Nobody needs to be stealing each other's labels.