I have personal experience with this and can verify it as being completely accurate.
I had a web development company that exploded - meaning from 3 people to 35 employees in under one year. Our website was getting enormous amounts of traffic due to our customers going there for info, new customers checking us out, etc.
As time went by, we eventually closed down as we could not keep up with the work. We sold all our hosting contracts to a third party, and our corporate website was deleted.
I decided to revive it later on (maybe 6 months down the road), so I uploaded the whole site (from a backup) - old Google Analytics intact. The site was previously ranking quite well for some keywords when we were still open. After putting up the new site, Google saw that there was no traffic, and it disappeared into thin air. Never resurfaced again to this day.
Damn right Google looks at your Analytics. They want to know your traffic/bounce rate/duration/page views. Why else would they have acquired that company?