History is one element and there is enough sufficiently backing the ability of the F-4F to use AIM-9J to allow it in game. If we are to limit everything to purely historical armament, in service or ownership, all tanks would have to loose 50% of the shells we have in game and we would have to remove about 50% of the vehicles in game. First and foremost we are a game. Not a 1:1 simulator.
You are correct that the material is very clear on F-4F, in that it can carry the AIM-9E and J. Both its pilot and weaponry manual show it:
1) GAF TO 1F-4F-1 Flight Manual, 15 October