I'm wondering about this Anne. The parents she's attached to had a well-documented daughter named Anne who married Sr. Anthony Cooke. There is nothing in the About section of this Anne documenting her or her connections. If there is documentation for this Anne (FitzWilliam) Swift being the daughter of Sir William Fitzwilliam, Alderman & Sheriff of London and Anne Fitzwilliam (Hawes), it needs to be put in her About section to eliminate any uncertainty. If there is no documentation, especially given how well the rest of the family is documented, it would be best to disconnect her from unproven family ties so the Geni pathways aren't incorrect.
I Googled and found very little on this Anne. In fact, her Find-a-Grave page:
https://www.findagrave.com/memorial/150657613/anne-swift
doesn't list any parentage for her and makes it appear that Taylor was her maiden name. There is no hint at a FitzWilliam connection.