As with all cheeses, "parmesan" labeled cheeses will also vary in quality. Go for what your wallet + taste buds tell you to pick. There really are good quality "parmesan" brands out there. Maybe not the cheapest stuff in your grocery store, but as long as you know what you're getting...
I have a philosophy: if it's made from real milk and by craftspeople who respect the product and the customer, then DOP is not necessarily the only marker of quality cheese.
edit: Here's an anecdote: A few months ago I travelled to the USA (Detroit) for a friend's wedding. Most of the food after the ceremony was from local producers, either acquaintances or good friends of the couple. My friend (who is also not from the USA) told me to try some of the charcuterie and cheeses on one of the tables and to tell him what I thought (we're both from Spain). The parmesan on that table was just perfect. Obviously not the real deal, but you could see the texture: the crumbly-ness (is that a word?), the little crystals cracking in your mouth, the aroma... I would not have guessed it was local produce. The same goes for the cured meats (some chorizo, and some cured ham, with a profile somewhere in between serrano and prosciutto). Really good stuff, and definitely not DOP.