Your boss is an idiot. Sorry but he is.
How on Earth is he expecting an internet aware application from not using the internet? It's like expectinga browser to work without an internet connection. Sure it will work, but you won't have much use of it without connection. It's the same with avast! or any antivirus in that matter.
It has to check connection here and there to operate correctly. Either for definitions updates, CommunityIQ queries, submission of susipicious files, WebRep etc etc. Let alone apps that rely on cloud technology and constantly connect outbound and inbound with vendors servers.
Besides in these days when everyone and everybody hack other apps and reverse engineer them, it's very unlikely that any company would be stealing data like this and not get in the news quickly. As someone would spot something like this very quickly. They have before and they will in the future.
If you want to enforce YOUR policy for YOUR network, you have to enforce it on your own using packet filtering, port blocking or just firewall alone.