I'm aware of tipping based on the full amount, and I agree with the practice. But there are other nuances to it that people can quibble about. For example, it's not expected to tip on drinks according to some people.
The bottom line is that tipping is a custom and an etiquette. These things vary quite a lot from location to location. It's surprising to me that someone would assert that there's really only one proper way to do it in a country as big as this.
Emily Post, for example, says to tip only on the pre-tax amount of the meal plus 1-2$ per drink and nothing at all about coupons.
Edit:
Still doesn't change the fact that Groupon has a rather nasty habit of taking advantage of small businesses and generally screwing them over. But that's a mixed bag also. I use Groupon a lot and find them to be a great source of places with generally well-meaning owners who are a good alternative to large corporate chains and work hard to keep me coming back.
My ex-girlfriend used Groupon to find ways to go cheap and took advantage of it with absolutely no intention of ever going back to see anyone a second time. Her repeat business could not be bought with any exceptional level of service.
Ultimately, it's a business decision the owners have to make for themselves. The problem for Groupon as a company is that their largest appeal is for people who are going to be a bad business decision for the owners using their service. It's a bad model, and it's clearly failing, so that means things are working exactly as they should.