I'm not trolling, I just don't think you've really thought about what "authentic" could mean if you don't have identity, which is a distinct problem.
For Alice there's no difference between a Bob whose identity you don't know and an Eric whose identity you don't know, they're each just another anonymous party.
Eric can't fool Alice and Bob into believing they're talking to each other, because they're using separate channels and identity systems will bind to the channel. Suppose Bob provides his identity, that's bound to the Eric-Bob channel, when Eric copies it to the Eric-Alice channel it's just obviously fraudulent, he could have made his own fraudulent claim of Bob's identity just as easily.
For Alice there's no difference between a Bob whose identity you don't know and an Eric whose identity you don't know, they're each just another anonymous party.
Eric can't fool Alice and Bob into believing they're talking to each other, because they're using separate channels and identity systems will bind to the channel. Suppose Bob provides his identity, that's bound to the Eric-Bob channel, when Eric copies it to the Eric-Alice channel it's just obviously fraudulent, he could have made his own fraudulent claim of Bob's identity just as easily.