How long did Rin live? We've never seen Rin in any of the flashbacks at the village AFTER the war. This suggests that she died during the war, some time after Obito "died". Let's play out one scenario that works:
1) Obito "dies", but as he's covered by rocks his MS awakens from his feelings of loss, and he is able to phase out of the rocks to safety.
2) Kakashi, Rin and Minato move on to the next battle. Minato goes off to do his thing. Kakashi is still hot-headed and not thinking clearly and Rin dies.
3) Obito witnesses Rin's death and sees that Minato is to blame for it (not Kakashi)
4) Obito decides not to go back to see them, because he blames them for her death. Instead, he wanders around until he joins Akatsuki, is "reassembled" by magic Zetsu slime, and eventually becomes a second-in-command to Madara and pretends to become Madara after his death.
This is sort of reasonable, and it does explain a few things:
This is why "Tobi" fought Minato instead of just taking the fox and running away. If he blames Minato for Rin's death, that explains why he would want to kill Kushina (and baby Naruto), and why he wouldn't have focused on capturing the Fox and taking the Fox away to Akatsuki headquarters.
This is why he wants Naruto and Sasuke to fight to the death: Either way he wants Kakashi to lose a student, and he wants Naruto to die because Naruto is the son of Minato.
Point #3 above is why he didn't say that he blamed Kakashi this chapter. He really blames Minato. Kakashi just didn't stop it.
Why is Obito "Nobody?" Because he's a person who is supposed to be dead. An Uchiha without one of his sharingan eyes. A person who loved a girl who is dead. A "hero" whose last wish was to protect Rin and she wasn't protected. Basically, everything he was, everything he stood for, all the hope he had and all the people he trusted ended up not being enough to keep a single girl alive. This is why he rejects hope and why he rejects reality: If you give everything and that's still not enough, then giving anything is worthless.
I still don't like the Tobi=Obito reveal, but it does make some sense if you think about it and his motivations are a little bit contrived but they can be explained.