This is a funny thread as you are absolutely right and I never noticed people doing that before.
In my situation, it depends on the social situation. With people that I know very well, I'll look them in the eye at the start of the conversation and occasionally throughout the entire conversation. If a stranger comes up to me, I will have more eye contact with them.
Something to note, and I don't know if its most hearies or just me, but I'm very observant as to what is happening in the room around me. While I may not make eye contact with you, its because I'm watching the door....or the guy up front reaching into his jacket. I've always been like this and it isn't a police thing. When I'm in a conversation and I"m making 'eye contact' in most cases, I'm watching over your shoulder 
This is one thing that will prove difficult for me when chatting with the deaf.
