Does the internal examination of a woman invalidate the doctor's ablution?

Ablution is invalidated upon touching the private parts without a barrier, based on the hadith: "If any of you touches his private parts with his hand, and there is no barrier or covering between them, then ablution becomes obligatory upon him." The majority of scholars have appended to this the touching of another's private parts without a barrier. Malik restricted it to the intention of pleasure, while Al-Shanqeeti and Al-Adawi favored invalidation absolutely, due to the generality of the hadith: "and one performs ablution after touching the male organ." However, touching the private parts with a barrier does not invalidate ablution, based on Al-Shafi'i's statement: "If a man touches his male organ with something between him and it, as long as it is not directly accessible to it, then ablution is not required of him." Caution should be exercised when dealing with women; a male doctor should not look at or touch a woman except what is necessary, without being in seclusion, and when it is not possible to do without a male doctor. Medical institutions should provide female staff to treat women.