there might have been cultures where in certain cases being raped is less of a status hit than consenting to sex with the same person, in which case someone might falsely claim to have been raped to avoid the status hit.

In many cultures including at least tradition Judeo-Christian ones adultery is a major sin and a betrayal of one's husband but being raped is not the victims fault so she can't really be blamed.

Yes, this did cause some adulterers to claim to have been raped, heck fake rape allegations happen to this day.