F-4 stab anhedral was for aesthetic reasons
One wonders where such stories come from.
The F-4 design was preceded by the F3H-G mock up. Photo below. The wing had no dihederal, nor the tailplane, as was also the case with the preceding in service F3H "Demon". The G never went beyond mock up stage. Within McDonnell the G went by the designation Model 98B.
After much wind-tunnel testing, it was found that the fighter would encounter severe stability problems at high speeds and would as a result probably be limited to speeds below Mach 2. At issue was the rolling effect of the outer wing panels in yawed flight. In order to correct the problem the tailplane was given 23° of anhedral, an increase from the original 15°. This gave the necessary degree of stability, but still left the tailplane free of the jet exhaust and turbulent wing wake. So became the first flying Phantom, the YF4H-1 (Model 98S).