itsthatKat
There is no such thing as "Jewish blood", at least in a biological sense. There are Jews of all "races", but Jewish spiritual lineage travels through maternal lines, not paternal. If their mothers weren't Jewish, they aren't Jewish.
I'm using "Jew" in the secular sense and a Russian context (since we're discussing Soviet migrants). In Russia if you were a Jew, not by religion but by ancestral links to the Yiddish-speaking descendants of the Israelites (who I'd call ethnic Ashkenaz Jews) , then you would have this as your "nationality" printed on your passport. Not only that, but since you inherit your father's surname your Average Joe (or I suppose Average Ivan) would view you in the context of your father's surname. Therefore, while someone with a Jewish dad would be discriminated against, such a thing would be unlikely to happen to someone with a maternal Jewish grandma or great-grandma.
And in the Russian language, the word Yevrei does in fact imply a person of Jewish/Hebraic/whatever-you-wanna-call-it ethnicity. The term Yudei, which is a rather uncommon word, means someone who practices Judaism. That's just the way it goes in Russia. If you're name is David Abramovich Kaplinsky no one is going to ask for your maternal records before beating the crap out of you.
The Law of Return was supposed to save people from anti-Semitism. Therefore having it only based on Orthodox halakha would be silly. Imagine if someone was of overwhelming Jewish descent, but their mother's mother's mother turned out to be gentile...to reject such a person from their ancestral homeland would be ridiculous.