You said something about ‘no basis in truth’?
Yes I did. Nothing you posted provides a basis to support her claim about this woman's daughter. Nothing you posted even supports a claim that Gardasil was responsible for the events you listed - it might infer a correlation, but does not provide evidence to support that inference. Without more evidence, she was irresponsible to make an unsubstantiated claim. But regardless, I still don't see how this has anything to do with sexism.