Contrary to popular slogans, there is in fact such a thing as bad publicity.

I don't think Groupon intended this reaction, I think their ad agency was stupid and Groupon had a blind spot because they knew what they meant to say. As opposed to the message they actually did communicate.

The weird thing is that they didn't even have to do anything edgy at all. They have a good product that people naturally want. All they had to do at this point was explain what they do.

Sure, but I am in the startup space and hear about Groupon every other day so I have a bit of selection bias. Also if it was to create controversy then it negates their response to the uproar.