Is it permissible for a male doctor to treat an unveiled woman accompanied by a man she claims is her mahram, while doubting her truthfulness, especially if not treating her would lead her to another male doctor who might not adhere to Sharia rulings in his treatment?

It is permissible for a man to treat a woman, with controls and conditions. There is no difference between a woman who displays her adornments and others, except that the one who displays her adornments sins if she does not cover herself, and the doctor must lower his gaze. The man whom she claims is her mahram is considered a justification for her to enter with him to the doctor, either because he is a mahram or another man with whom khalwa (private seclusion) is negated if temptation is secure.