No, I'm not mistaken. You might want to reread my message and check the sources I've cited. Also, take a look at

http://www.themayflowersociety.com/index.htm

http://www.mayflowerhistory.com/index.php

http://www.alden.org/

It's easy to be mislead by information that you find online, but many people have researched these families. I don't pretend to be an expert, but I like to think I listen to the people who are experts.

Best wishes,
Karen