The F4F-4 was clearly inferior to the Hurricane II as a fighter aircraft so any successes that it had were due to the unique tactical situations in which it operated. Logically, a better performing aircraft, should do at least as well.
Putting aside the rivalry for the moment, can you really be sure all this is true?
This is I think one of the dilemmas of understanding WW2 air combat, or any military history. How much of what happened is down to morale, to weather and environment, to logistics, to training and discipline, and just plain luck, and how much due to the properties and performance of kit? This is an issue going far back into history - how much of an advantage were iron spearheads over bronze? How much did the longbow matter at Agincourt compared to the weather and the terrain?
Once you get into as artificial an environment as four miles into the sky and 300 mph, the kit starts to matter a lot more. One man with a pointy stick - or one man with an automatic rifle - is only so much different than another. But we know for sure that an I-16 was at an almost insurmountable disadvantage against a Fw 190. But the skill of the pilot, the rain or fog, the quality of maintenance, training and discipline, all these things still did matter of course. It's hard to determine precisely how much. But we still see aces flying Buffalos and Fiat G.50s in 1943.
When it comes to Hurricane II vs. F4F-4, I don't see such a sharp difference in performance. Speed is about the same, Hurricane turns better, Wildcat probably rolls slightly better (I show Hurricane Mk I at 64 degrees per second at 230 mph, 30 lbs of force, Wildcat at 69 degrees per second. Hurricane Mk II is probably a bit worse), dive is a bit confusing in light of slaterats evidence, but pilots seemed to say that the Hurricane dived poorly. I don't know how to reconcile that. Hurricane climbed a bit better - so long as the engine was performing properly. But there are a lot of reports of overheating. Hurricane also had a radiator which made them a bit more vulnerable to gunfire. Japanese pilots were trained to target the radiator.
The Hurricane had heavier guns, but only 60 rounds of ammunition for the 20mm when you are talking about the IIC. I would say therefore that the Wildcat is actually a bit better armed. (I know that many wouldn't agree with that). The four wing cannon apparently also affected maneuverability on the Hurri.
Overall, I'd say on paper performance looks similar. I certainly wouldn't rate the Hurricane as better. So the difference could be training or circumstantial, or even luck, but considering the number of iterations I'd say there is a pattern which shows the F4F had the edge.
For example, many papers have been written about Agincourt. It has been proven definitively that longbows can't shoot through iron armor. Elaborate tests have been done which show the extreme difficulty of the environment for the French. Some people concluded that the longbow wasn't really a factor. But the thing is, there was more than that one incident. English victories at Crecy and Poitiers also hinged on the longbow. So did victories in Scotland and Flanders and as far away as Spain and Italy, and Lithuania. Taken together, it's enough variety in all the other random factors to assume that the longbow really did make a difference, just like everyone said it did back in the 14th and 15th century.
I don't think the relative success of the F4F was a fluke, though I can't be certain what the actual reason was. I don't think it was pilot training because my understanding is that the FAA and RAF pilots were well trained.