This is a nit pick and doesn't change your argument, but Alpha Centauri would not have been our neighboring star system for a billion years. Stars move relative to each other in our stellar neighborhood at about 30 km/s, or one light year every 10,000 years.
Yep, good reminder! Of course, as you point out, it doesn't change the argument because probing (or simply direct observation, if they must hide) would still be trivial, both at larger distances when we weren't quite neighbors and on the shorter timescale when we were. Trivial next to mustering an interstellar invasion fleet on the turn of a dime, at any rate. Besides, if they were itching for a fight then the original "decent fraction of billions of years" timeline still applies to the question of "why didn't they grow and colonize?"
