During the last year my parents (who are 3rd cousins) and I did theMy experience as a descendant of eastern European Jews is that if
your longest block of shared dna is 9 cMs, you are unlikely to be able
to prove a relationship between this neighbor because the records do
not go back far enough. If your ancestors were in western Europe or
the U.S. a long time ago, it is possible.
This dna tracing is a combination of science and statistics.
Either could be incorrect, and both are being refined as we speak and
as the testing services' databases become larger.
This is just a guess, but I think the explanation for the match
with you but with neither of your parents is this. Whatever dna you
share with this neighbor came about half >from your father and half
from your mother. The amount shared with neither of your parents wasenough statistically to get them over whatever threshhold of
relationship FT DNA has. Put together in you, it was enough.
San Diego CA