Before I uninstalled the "full" v6.0.0 (files dated from May last year) in favour of the "basic" version 6.0.1, I did some checking on this issue:
First off, I changed the firewall rule I had created a while back to inform me whenever this connection was attempted. Then I tried Acrobat with most of the pluggins removed (as outlined in my other Acrobat thread, "Speeding up ..."). Result -> Acrobat no phone home. Add the pluggin's back in and the result -> Acrobat phone home. So it was one of the pluggins. I then quickly tested by removing a few possible offenders, but had no luck as Acrobat still tried to phone home on these attempts. Although I am very puzzled why one of the pluggins wants to phone home and even more so by the fact that I never saw anyone else report this behaviour, this isn't terribly important, and rather then wasting anymore time in tracking down the culprit, I did the sensible thing and moved on to the next task at hand.
Namely, I uninstalled the full version and then installed the basic v6.0.1 and the result was ..... (big suspenseful pause) ... Adobe no phone home. So I'm happy.
I guess the truth is out there, but I'll never know. Here's to hoping the basic version doesn't develop any bad manners over time.