I see people saying "what if rin is possesed or a fake?"........what if the kakashi is the fake?
or what if they are both fakes just to get obito stirred up?(although this i doubt)
I have the bad feeling that it was a concious decision, why else would kakashi in previous chapters ask if obito blamed him for what happened to rin.
I think obito might jump into the situation, neither will recognize him, and when he tries to explain who he is, they will try to make him go away and call him a liar because they "know" he died. Thus making him feel like "nobody" and that there is no reason to return to the village (on top of the love of his life dying).
Maybe kakashi and rin are being forced to fight to the death by their opposers.
Lol more possibilities, very unlikely as they may be, danzo or orochimaru are involved.