> Thinking is, after all, an action, and all of their actions are identical. Therefore it seems like your example assumes Alice's behavior both is and isn't identical to Bob's.
By your logic, I was heterosexual for my entire young adult life when I actively worked to deceive people from realizing my actual orientation :P
People employ dishonesty for lots of reasons, and in myriad ways. Sure, in this thought experiment, perfect indistinguishability means the difference is inconsequential. But you can use crises as an oracle to observe different behaviors, and thus undermine its indistinguishability.
To keep the cryptography going, this is like an active vs passive attack. Sure, it's IND-KPA, but is it IND-CPA or IND-CCA? Perhaps not!