It's an interesting story that TS is misrepresenting. Roe v. Wade wasn't based on a false rape claim. But there was one in connection with the pregnancy giving rise to the case.
Basically, Jane Roe (McCorvey) got pregnant and wanted an abortion (abused kid with problems, was married off and an alcoholic by 16, two previous children taken from her).
Texas law forbade abortions except when there was a danger to the life of the mother, but McCorvey mistakenly believed that there was also an exception if the pregnancy resulted from rape. So she attempted to obtain an abortion by claiming that she had been raped by an unknown person (although she had previously been raped by a family member, it was not what caused this pregnancy). She did not get one.
She was then contacted by two attorneys who were seeking a plaintiff to challenge the strict anti-abortion laws, at which point Roe v Wade began. The rape allegation did not play any role in the case.