They are not saying that the X chromosome mutates to Y, but rather saying that XY doesn’t define the sex. For example, some people with XY are born with female genitalia and look female their whole lives. Sometimes they don’t find out they are XY until trying to have kids and are unable to. It isn’t like the X changes to Y over time. That isn’t possible.
I think you may have misread. The PHD isn’t saying that XY becomes XX, they are saying, genetically, a person carrying XY can be a cis woman. Biologically, XY doesn’t determine the sex.