We're not making that assumption.
We're talking about A because Israel extends certain privileges only to A-jews. Orthodox jews only accept A-jews.
If there's some explicit cutoff date (N generations back? 1900?) before which there's no brand attached to not having a jewish mother then I guess we should talk about A' instead.
No. If you convert today by Orthodox standards, then you will be recognized by Israel and Orthodox jews as a jew. You most certainly can do it, you just have to follow stricter standards and there is no reason to believe that such standards were not followed then.
"This resulted in several hundreds of thousands of persons fitting the above criteria immigrating to Israel (mainly from the former Soviet Union) but not being recognized as Jews by the Israeli religious authorities, which on the basis of halakha recognize only the child of a Jewish mother as being Jewish."
and http://en.wikipedia.org/wiki/Birthright_Israel "Eligible individuals are those who have at least one parent of recognized Jewish descent."
Also, I feel like maybe I wasn't clear. You are considered Jewish by even the strictest standards if you (1) converted or (2) can trace matrilineal descent from ancient Israel or (3) can trace matrilineal descent from a convert.
What I'm saying is that when Jewish men showed up in Southern and Western Europe, they seemingly got hitched to a lot of local women. How do we know the majority of those women didn't convert?