Over the years I have converted pilots from very varied backgrounds onto a wide range of types, including fast jet pilots onto ME types and vice versa. I have always found the differences in how different individuals perform fascinating and have tried to work out why.
The starting point in the nature vs nurture discussion is what is meant by a natural pilot? To answer this we need to look at what the piloting task is. A pilot controls the flightpath of an aircraft and has to make control inputs to achieve what is required. He/she must make the required control inputs to initiate a manoeuvre then scan the required cues (visual attitude, ASI, altimeter, g meter etc) in a pattern relevant to that manoeuvre and then must correct any errors in the required flightpath with further control inputs.
A natural pilot is one who intuitively has the required scan pattern at a high rate such that he/she can detect errors in the flightpath very rapidly when they are still small and then has a valid muscle memory to make the required correcting control inputs. Muscle memory is, arguably, a learnt characteristic (nurture) and some people are more adaptable than others ie. learn more quickly. In this respect a 'natural' pilot could be considered as one who acquires the correct muscle memory very quickly such that, effectively, it becomes intuitive/sub conscious. If the muscle memory and error detection is intuitive it will reduce the amount of mental capacity required to fly the aircraft. If this is not intuitive (ie. a non-natural pilot) it can often be learnt but will require more mental capacity which may then become a limiting factor for what roles a given pilot can undertake.
In addition to the pure flying task, a pilot has to make decisions (airmanship) and complete secondary tasks (eg. mission system operation). Mission system operation inevitably is learned (ie. nurture not nature). Decision making requires a mental model which also is usually learnt (again, nurture). However, the ability to complete the decision making and secondary tasks relies on mental capacity and this does vary markedly between individuals. Therefore, a 'natural' pilot who has average mental capacity may well have the spare capacity to make the decisions and complete the secondary tasks required for most if not all missions. However, a non-natural pilot with the same mental capacity may, for some tasks, become task saturated such that he cannot undertake high workload missions.
Some aspects such as employment of checklists and SOPs will always be nurture. And then there is CRM (which does still apply to single-seat formation and multi-aircraft operations). Some of this is nurture but nature plays a major part here; this encompasses all roles but I have heard of cases where some of the pilots who are more challenged in this respect were sent single-seat if they had the other abilities required!
To return to the original question regarding nature vs nurture and fighter pilots, the fast-jet missions are typically high workload. Therefore, fighter pilots need to be either natural pilots in order to have the spare mental capacity to perform the decision making and mission tasks or they have to have high mental capacity in order to absorb the increased workload resulting from learned/nurtured pure flying skills.
The interesting case is when an individual has natural flying ability but relatively low mental capacity such that they will never have the spare capacity for the high workload secondary tasks of some missions.
All of the above is personal opinion based of many years of observation. I am interested on the thoughts of you all on this.