The money being lost on the Groupon is a sunk cost, so you've got:
Option A: Lose money on the customer, treat them like second class citizens, probably lose the customer forever, possibly have the customer tell all of his or her friends how bad they think the business is.
Option B: Lose money on the customer, still treat them just as well as any other customer or even better and try to convert them into a repeat customer and/or organic spokesperson for your business, recoup the lost groupon money over time through repeat business.
I can't speak for everyone but I know that if I'm an option B customer, I'm going to be an enthusiastic spokesperson for the business. Getting a great deal and good service early on is a good way to convert me to be a customer of yours for life (early impressions really stick with you, sort of the reasoning behind buying the first round of drinks, you probably don't need to buy another drink all night because you're the cool guy who bought the first round).
So all-in-all, I don't think all the blame of having Groupon customers treated badly (if this even exists as a real thing and isn't a perceived occurrence that isn't statistically a real thing) can be placed with Groupon.
I suspect at least part of it is likely just the fact that a lot of businesses have terrible customer service these days (probably due to a number of factors including low wages, races to the bottom on margins, etc) and as a customer you would have been treated pretty poorly anyway but the groupon thing gives you something to latch onto as far as reasoning it out.