What I was getting at is that the current setup allows for side-channel methods of getting information on your opponent. (Digging to find their identity, reading their Facebook page, etc.).
While I accept that this interaction could be one of many between the AI and the researcher, this can be simulated in the anonymous case via a 'I was previously GatekeeperXXX, I'm looking to resume a game with AIYYY' declaration in the public channel while still preserving the player's anonymity.
By the way, wouldn't Omegle with the common interests specified as AIBOX basically do the trick?
AI Box Experiment Update #3
Tuxedage (AI) vs Alexei (GK) - Gatekeeper Victory
Tuxedage (AI) vs Anonymous (GK) - Gatekeeper Victory
I have won a second game of AI box against a gatekeeper who wished to remain Anonymous.
This puts my AI Box Experiment record at 3 wins and 3 losses.