Margery (Pierce) Eames - Disputed origins

What is the evidence Margery Eames was a daughter of John Pierce & Maud Pierce

“An Account of the life of Captain Anthony Eames (1595 – 1686) Churchwarden of St Georges Church & Constable of Fordington Manor.” ©Compiled by Michael Russell OPC for Fordington December 2009 (Revised March 2010 - updated May 2011 with additional information on Jonathan Eames (1628-1702) update Aug 2015 to take account of Anthony, Margery and their son Mark being beneficiaries under the Will of Rogere Kete (d.1620) < link >

Marriage to Margery Pierce - circa 1616 (Updated Aug 2015)

Lets not get ahead of ourselves. Anthony is said to have married a Margery Pierce (12 ) about the year 1616 but I have not come across any firm evidence to confirm that this was her maiden name. In fact it was not until August 2015 that I located any evidence this side of the atlantic to confirm that her first name was Margery. …

Can someone explain what can’t be found in English records?