There is still a host though, I was under the impression that the server simply accepts all the connections from all players, regardless of their NAT status then sends that data to the game host in 1 big sweet lump that is free of NAT compatibility issues.
It's just regular P2P with the NAT issues removed, you'll still get host advantage because the Host's machine is having the final say on every shot fired.
But in P2P, doesn't one machine act like host and determine damage, hits, scoring, everything? In Killzone, YOUR PS4 determines damage taken, your position on the map, hits, etc. The host is only receiving scoring information. It's really not difficult to understand.
"Almost all logic relating to you (e.g. moving, shooting and taking damage) runs on your local PS4, with only a very small portion of the game logic (i.e. mission/scoring logic) running on the session master, one PS4 in the game selected for its connection quality."