This is a good, clear explanation of Groupon's business model. I think one of the following must be true: 1) Groupon does not realize the Ponzi-like nature of their business, and this led them to turn down Google's offer. 2) They do realize it, but common sense was outweighed by hubris -- they thought they could keep it going until the IPO, or maybe the next offer from Google. 3) They're really, really smart and are working on plan B. That would be one hell of a pivot.
Excuse my ignorance but at what stage in an acquisition do you have to open your books to the acquirer? Any chance that they didn't want to give google this opportunity?
Google would have reviewed their books and could easily see how shady it was, but likely didn't care. Look at Youtube and how long Google bankrolled them before they hit profitability. Adding Groupon to their portfolio and integrating it with existing and upcoming products would have been a big win for them.
I'm guessing what others have said is right: Groupon management figured they could get more value by pushing for an IPO. They're likely right, although I can't see Groupon surviving long afterwords. If Google had bought them, then it had a chance to be a long term company. Now, it's an excellent investment for the founder and early investors, and the public will get screwed.
add to that, the primary cost of youtube is probably bandwidth; and I believe Google probably pays less for bandwidth than anyone else; Google is uniquely suited to make the YouTube model work. On the other hand, the big cost for groupon seems to be salespeople. Unless google can replace flesh and blood salespeople with something automated, that wouldn't be nearly as good of a fit. Google doesn't have cheaper fleshy sales people than anyone else.
edit: on the other hand, what if google was buying the fleshy sales people? what if that is what they wanted? I mean, groupon is doing okay at penetrating the small local business market in a way that google isn't.
I'm betting on #2.