First, Ill agree with the people stating the manga states kakashi "let" rin die, no where did it say "kill". Also people need to remember, Kakashi Chidori is a jutsu that protects its comrades, not kill them. As shown when kakashi became upset when sasuke used it on naruto. Also I agree with the people saying that kakashi looks the same as he did when Obito was thought to have died, perhaps the last image he saw of him was used as a model. Lastly people are saying that Obito saw it through his sharingan.... Are you all forgetting the for one, obito is wrapped around a zetsu and that half of his obito is the same as zetsu, you also need to remember that zetsus have the ability to record and transmit everything they see.... So it could be possible that zetsu( or someone as to not suspect madara or zetsu being involved) "staged" this attack to kill rin using a mold of kakashi as the weapon and then relaying that encounter to obito... It is very possible. we have no idea how zestu records and transmit what he see.... but he did say it was some type of telepathy!
I am willing to bet we will see a injured kakashi show up just as Rin is dying and see whats happening but be unable to save her.... thus "letting" her die! Remember zetsu said they were surrounded by mist ninja... WHERE ARE THEY????
Another observation... IF kakashi did kill her, he would have no reason to ask Obito if he blamed him... WELL DUH I blame you, you stabbed her!!! cmon people see how that doesnt make sense lol!