Technical, if netstat doesn't show any established connections (other than the expected ones for your browser etc) you are at least safe.
It could be ip spoofing, have you cleared out your temp internet files/cookies?
Also try from cmd ipconfig /flushdns
I recently switched to Outpost and don't have any problems with Avast's servers at all.
Edit
I noticed in an earlier post your screen shot. I use the free Outpost firewall and can't find anything like that in my version, the blue shield might be the clue.