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.