I am not an expert, and defer to anyone who is :)
My understanding is "Yes". If the profile indeed represents her, then we extend the courtesy of removing the information from public display at her request.
I believe locking up the privacy level so that it is unlisted or similar fits the bill and appeases everyone. We can have unlisted profiles of anyone we wish and it does not affect anyone else. It is essentially the same as deleting it.
On identifying the profile as being her.... it is now simply up to the profile manager to determine and state. If she says "yes, it represents her" then she will have to make it vanish. But, if she says "no, it's someone else" then there is nothing to be done.
Obviously, someone cannot ask for every profile of the same first and last name as theirs to be removed from WikiTree. One guy named John Smith born in the 50s could ask for 50+ profiles to be taken down, when in realty only one could or should represent him. The way WikiTree displays the birth-dates as only a decade really helps eliminate many privacy issues.
That's what I'm thinkin' :)