Rape or not?

If someone goes into woman's bedroom, pretends to be her boyfriend and has sex with her, then when she finds out he's not her boyfriend, it becomes rape. But if someone meets a woman, pretends to be Brad Pitt, goes to her bedroom and has sex with her, then when she finds out he's not Brad Pitt, it does not become rape.
The falsehood in the later instance would not invalidate her consent. In other words, here are two lies, identical in their intent and in their result. One is a crime and the other, however deplorable is not.

Among many things from the book; Ill-Gotten Gains: Evasion, Blackmail, Fraud, and Kindred Puzzles of the Law.

It is an inconvenient truth that not all strippers use all their money for college funds so they can become sexy librarians.