K. I'll chime in as another non-competing autocrosser. Del, Michael D, or any of the others who run the nationals have more valuable input than me.
I think in a broad sense you are right that the 2 biggest factors are tires and driver skill. Those amount to 1 (or many cases more) seconds in run times.
However, margins of victory are much smaller. When a tenth of a second seperates the first few positions, can we say for sure that the giant spoiler on one car didn't make a difference? And if we honestly believe it didn't, why was it installed? Just food for thought.
As Del pointed out, his car and probably many others in DMod are results of many years of optimizing, changing, etc... At that level, every improvement is there for a reason. Common sense tells me a Caterham in stock trim that was purchased 10 years ago, and is setup properly, will still be slower than a winged car optimized for autox, given equal drivers, tires, power to weight ratio.