While the example is basically correct, I fear it might kill more minds than enlighten then.
By doing this you basically force breach a compartment in someone's mind.
It is difficult to address the issue of sincere versus pretended socially desirable beliefs without reference to the individual consequences thereof, which needs a reference, however delicate and indirect, to particular consequences that happened to some particular individual, a reference to events that happened to a particular individual that would not have happened if socially desirable beliefs had been true.
This is thread where I'm trying to figure out a few things about signalling on LessWrong and need some information, so please immediately after reading about the two individuals please answer the poll. The two individuals:
A. Sees that an interpretation of reality shared by others is not correct, but tries to pretend otherwise for personal gain and/or safety.
B. Fails to see that an interpretation of reality is shared by others is flawed. He is therefore perfectly honest in sharing the interpretation of reality with others. The reward regime for outward behaviour is the same as with A.
To add a trivial inconvenience that matches the inconvenience of answering the poll before reading on, comments on what I think the two individuals signal,what the trade off is and what I speculate the results might be here versus the general population, is behind this link.