Re the Syrian Jews, Rabbi Raymond Beyda (who is a Syrian Jew, and who has many good "shiurim" (torah lessons) on learntorah.com) said in one of his shiurim that the Syrian Jewish community has some sort of "by-law" (he used the Hebrew word, but I cannot remember it) about members only marrying within the community. That sort of thing goes beyond torah law, so maybe their standards regarding only having a Jewish mother do too.
Just a thought ...
