In Doctor Who, S11E08, when the Doctor is challenged in 1600s Britain she whips out her psychic paper, which says that she's an official Witchfinder General. Thus, Mistress Savage bows to her authority.
However, the only Witchfinder General (self-proclaimed) in Britain seems to have been Matthew Hopkins. Anyone who had heard of this office would have known who held it, and that he wasn't a woman. In addition, the Doctor and her companions are clearly dressed in rather odd clothing, such that they seem like foreigners or actors (as King James mentioned).
King James, also, while he can't accept that the Doctor could be the Witchfinder General, believes that Graham is, although he should know even better, given his personal interest in the subject and the role of his writings in inspiring Hopkins.
Obviously, the psychic paper would have looked very official, but it doesn't override evidence.
Why was her identity so readily accepted?