Ok, here's my stab at this.
I think MO's theory wrt conservation of energy is, at least partially, correct, but he is misattributing where the energy comes from. Take this example:
You are flying an aircraft at 100KIAS directly into a 100kt headwind. Relative to the ground, you have the same kinetic energy. Therefore, stating that 'your kinetic energy is zero' is in fact correct (in keeping with relativity). An object's kinetic energy will only become relevant if it meets another object with a different level of kinetic energy (imagine two bullets fired from guns next to each other - if they touch, the effects are negligible; they have massive amounts of kinetic energy due to their high speed, but roughly the same amount as each other. If you now fire them directly towards each other, and they make contact, there is a very large energy transfer and the effect IS relevant.)
Now, initate a 180deg turn so you are flying directly 'out' of the wind. In the time it takes to make the turn, the aircraft will accelerate (the quicker the turn, the greater the acceleration) from zero to 200kts groudspeed and both you, and the aircraft, will FEEL the acceleration - you will percieve it as an increase in 'g'. Ordinarily, when an aircraft turns, acceleration, or 'g', is produced and felt. But the energy to create this acceleration comes from aerodynamic sources - the wings are directing some of the lift force towards turning the aircraft, so to maintain constant IAS and height, some extra energy must be added (more thrust) to provide more lift at the same IAS - total energy is conserved.
In the case above, the energy to accelerate the aircraft (relative to the ground) comes NOT from the wings, but from the air (the air 'behind' the aircraft will slow down relative to the ground). Therefore, although you will feel 'g' during the acceleration, the aerodynamic forces produced by the wings will not change - there is no increase in wing loading, despite the 'g' that you are feeling - therefore there will be no effect on IAS. Energy is, once again, conserved.
In JF's hovering Harrier turn, and Prince William's air race crash, there is a difference - they were both DELIBERATELY trying to fly with reference to the GROUND. The fact that PW crashed was nothing to do with IAS loss in a downwind turn, but the fact that he must have overloaded and stalled his wings in a turn, in an attempt to make the 'gate'. Bringing Helos into the argument will always complicate matters, as, when hovering or flying slow and low, they are almost invariably flying with reference to the ground.
Does that make sense? Or am I talking bollox as well? Makes sense in my head.