I don't think you can make a game like DayZ without griefing. The whole appeal of DayZ is its freedom. No arbitrary rules or restrictions. Removing PvP or limiting it to certain areas would ruin that. Humans are and always will be the biggest threat in a post-apocalyptic scenario. The interactions between survivors are what make zombie fiction interesting.
I do think that these games need to offer more incentives for players to cooperate and not just kill each other on sight. I think the ability to craft things and build structures would help provide that. Trying to clear out and then build fortifications to secure a town by yourself is essentially impossible. But a group of players working together could do it if the game provided the necessary systems.