Being raised a Catholic, I've got a clue. We were taught Peter (Saint) was the first, then a couple of men - then the Popes started.
Best of recollection - Society doesn't try to go that far back to claim anointing. They do, however, point to individuals or small groups during middle ages, such as Jacobeans, etc. who really tried, even in the face of death to keep God's Bible alive. And they succeeded, from what I've learned from Watchtower articles.
Now, it gets interesting with Russell, because he got quite a few of his ideas from Barbour and the Millerites, and Adventists, astrology, occult, Masons (Cross & Crown emblem) and study of pyramids. I don't believe that the Society counts these groups in their apostolic succession argument, do you?
Why they count Russell is becoming hazy light to me. In fact, a recent article with a BIG picture of Russell in it, said he had hazy light and quoted 1 Cor. 13:12, "For at present we see in hazy outline by means of a metal mirror.." I did notice that this scripture does not say "hazy light" but "hazy mirror."
This also would lead the reader to believe that the apostles were hazy also. But please read 1 Cor. 13, 1-14, I don't believe the writer was referring to hazy, changing, light. He was referring, always, to gifts and maturity - not changes in fundamental doctrines.
Even though the apostles and Christians didn't understand everything, to my knowledge, they didn't look to God, the stars and pyramids, etc. for their answers. I believe that's what the pagans did.