I would echo the other poster who mentioned the possibility of a non-parental event somewhere. I know that in my own case my Y-DNA testing shows absolutely no matches who share my own surname; all of them have the surname of Short rather than my own name of Elkins. The problem for me is that none of my matches are close relatives and from the number of steps, the non-parental event likely occurred back in the pre-immigration days back in Europe. As a result, the likelihood of ever isolating the Short individual in question is very slim.

Hopefully your own lack of DNA results isn't going to affect anyone's membership in The Mayflower Society!