The part that muddies the water is that in a massively multi-player arena it is possible to get kills without any air combat maneuvering whatsoever.
That's my point. It is all in how you define "best". The guy with the best K/D ratio could simply BnZ all day long being EXTREMELY conservative in his flight style and basically never die. Does that make him good at ACM/dueling?
Conversely, a duelist can be very good at ACM, but if he does not pick his fights in the arena intelligently his score will suffer.
So the above is my point, below this is just discussion. It's not meant to dispute whether or not dueling demonstrates pilot skill.
As far as "doing calculus before arithmetic", a few people have mentioned they can fight better than they can duel (you'd be surprised as for actual calculus and arithmetic; at my school students commonly complain that they are doing "MATH WITHOUT NUMBERS"). It's less variables, but may actually be a harder problem to solve because you don't have any aircraft advantages to use. E.g., when I fight 109K4 vs a P51D, I think to myself... ok... the longer I push this fight the more advantage I will have - my options are shallow spiral climb if he's behind me or aggressive maneuvering to stay on his tail if he's in front of me. In any case, once I have the positional advantage, I will not relinquish it.
Now, let's say it's K4 vs K4. Erm... I have no advantages! Hmm... what do I do? Well, in that case it all depends on what my opponent wants to do! It's more of a chess match because you have no dominant strategy you can use. If he turns very tight for angles, I can outclimb him and turn this into an energy contest - go up and stay out of reach of his guns. If he goes for a big climb for energy, I can pull just slightly more tight than he does and go for guns - it's a gamble.
See how this is already far more complex than an asymmetrical 1v1? In disimilar combat, you have well defined advantages and disadvantages, winning is simply a matter of flying to your advantages and avoiding your disadvantages.
Interestingly enough, that analysis may even further your case that dueling is a good measure of pilot skill. On the other hand... how do you measure pilot skill? Is it in how he strategizes in a duel? Or is it how he flies the aircraft to its advantages in disimilar combat?