The LDS online site has several items indicating the parents of Edmund Dalby were Richard Dalby and Margaret Underhill. The date of Edmund's birth is given as 1556/57. No original source or documentary proof is given.
Likewise, the Ancestry World Tree gives the same info several times, but the source is often given as the LDS. One person even traces Margaret Underhill's family back to the 1200s, but of course gives no source or documentation.
Some folks have traced Alice Woodward's family back to the 1300s, but again, no proof cited.