So uh... what makes elite hunts different from a FATE then?

[Felis]

Tell that to PvP players losing their ranks for having to change GC to play with friends.

They don't lose the ranks. It is still there in the old GC while they build up a new rank in the new GC.
Excluding them from pvp in this example would be if they can't use the old ranks and can't build up a new rank.

About claim or not to claim

free running open world enemies = no claim (in this game we use kill sharing, so don't be surprised suddenly. Everyone can attack. The claimer need only to attack once, the others need to do at least enough dmg)
force poped enemies = party/player reserved enemies (but you would know then where it is, no hunting down)