Wait wait wait... "evidence to prove you were playing the game properly"!? Mail them back and ask them how the flaming hell you're supposed to do that! I thought the burden of proof was on the accuser, not the victim!

But basically, you can easily address any of those points.

Erratic path behaviour of the craft - As you have correctly explained, that is due to network latency. It's commonplace if your connection is experiencing issues or indeed if the other person's connection is not up to scratch.
Travelling at speeds outside of the limits of the game - Direct them to some videos of Flash TTs and SLs on YouTube to show them exactly what is possible. That's subjective. Or better yet, do your own!
Random bursts of increased speeds - Turbos? Barrel rolls? It's a f*cking game mechanic! If they mean jumping back and forth randomly, then again, it's network latency.
An impossible race time for *flash speed class* - Video evidence of a race time better than your record. Plenty available.
Craft randomly gaining air and rolling - It's a game mechanic, it's even explained in the sodding game.

Sadly, sh*t like this is a problem now we no longer have anyone at SCEE who even understands the game, but the fact they've done this without any proof against you is quite frankly disgusting. I wish I still had some sway in the matter otherwise I'd just say give them my contact details.