This is pretty simplistic thinking. For all you know Groupon wanted the deal badly, Google walked away from the deal, and both parties agreed to go with the story that Groupon walked away so that it wouldn't kill their prospects of an IPO.
I don't think anyone had that feeling when the deal fell through. Many people were surprised Google was interested in the first place. Google had to consider the deal, after all Groupon was buying shit tons of advertising on Google at the time.
If you're company realizes a certain scale on the internet (i.e. a billion dollar valuation) there is a good chance the deal is going to get looked at by all the big consumer tech firms.
Groupon walked in to the negotiations with a publicly speculated valuation of 1B, and after the deal fell through they were being talked about somewhere greater than 5B, and got an extra investment from DST. Seems like negotiating with Google worked out well for them in that respect.
Notice how Andrew Mason never answers the question publicly about why they 'walked away' from Google.
That seems like a really complicated narrative for the two parties to fabricate. Isn't it just more likely that Groupon thought they were worth more than Google was willing to pay?