The arbitration they invited wasn't arbitration, it was a blackmailing. The only thing Armstrong would get to "arbitrate" was his own guilt, which has never been proven. The only evidence against Armstrong is hearsay from other cyclists who themselves were convicted of doping based on _failed_ drug screens and whom Armstrong beat time and time again. In legal parlance, these are called "unreliable witnesses" - similar to having a Mob boss' hitman testify against the boss himself.
One thing to note, however - the USADA doesn't have jurisdiction to revoke Armstrong's Tour De France wins. Only the International Cycling Agency does since it manages that race. The USADA is on a vendetta, pure and simple.