Being part of Google changes things as (1) Google can finance a money losing operation for quite some time and (2) Google offers integration into its huge ecosystem, especially its existing robust advertising network.
Thus Google brought a lot to the table in such acquisition which would increase Groupon's value.
This is the most insightful and concise thing I've read about the Google proposal so far. Google offering B$6 doesn't mean Groupon is worth B$6 on its own, it means it's worth B$6 to Google.
Google is not Warren Buffet investing in the hope of a passive but safe return on investment. Google was betting that Google + Groupon was worth more than Google + B$6.
Thus Google brought a lot to the table in such acquisition which would increase Groupon's value.