William Nickerson, of Chatham - Disputed origins

According to Bush, Richard L. The English Ancestry of William and Anne (Busby) Nickerson of Chatham, Massachusetts, and of Nicholas and Bridget (Cocke) Busby of Boston. American Genealogist (D.L. Jacobus). (Oct 2011 (published May 2013)) 85:246 < AmericanAncestors > page 250-251, the parents of William Nickerson, of Chatham William Nickerson, of Chatham were likely not William Nickerson & Alice Nickerson but rather, William Nickerson & Margaret Ward

As far as I can tell, the Nickerson Family Association does not have a position of his English ancestry:

https://nickersonassoc.com/2013/03/29/william-and-anne-busby-nicker...

I’ve set the Nickerson tree to the most current research. If anyone knows differently, please advise.