Peter

I think in part it will depend on whether C is part of, or close to, the hierarchy in which A has authority over B. For example, if B is A's secretary, and C is a visiting client, it would probably be hard for C to interact with A and B as equals during the visit (and possibly after it as well). But if C is a tourist who meets A and B in a nearby bar after work, there would presumably be little difficulty in C interacting with them as equals, because their local power differential will be meaningless to C.

If C is a super-authority over A and B, chances are pretty good that the relative parity of A and B is irrelevant. This also works if C is far under both A and B in a hierarchy. If A is the CEO of a multinational corporation and B is the deputy VP over domestic products and C is the high school intern working in the mail room... then the appropriate response from C to either A or B is "Yes, sir!" [* modified by gender if required]

Also if C knows A and B in a different context entirely. An example: My boss and I shop at the same supermarket, I have no expectations that my boss is treated differently by the cashiers.