Yeah, but here is the thing. Kakashi didn't even question it nor was it even brought up that he even thought about it being Obito. There were at least three clues to Kakashi right off the back with the Kamui being similar, this guy knowing of that technique that Kakashi has, and the fact that this man knew he was Kakashi.
I understand him not figuring it out, but to never question it seems rather funny.
I bring this point up because of the whole "Karin didn't recognize the mysterious man chakra so it can't be Kabuto" theory. From a writing standpoint, it would make sense for Kakashi never to question it because it would have given away the identity a long time ago.
Well Kakashi isn't like a hidden character. Remember, Madara is what Tobi called himself, so the world believed it since he was being haxer and what not. I mean imagine this.
Kakashi: I'll stop him with kamui
Tobi: Not so fast, that wouldn't work on me.
Kakashi: OBITO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
But seriously, Kakashi was already convinced that he was dead. Once they learned that Madara is not Tobi, then witnessing it, the puzzle starts to make sense. It's like you have the puzzle of obito, but it's 1000 pieces, so you have a hard time to place it. Once I told you it's Madara, you stopped working. But then you find out I lied. So now, it's back to work. Then you start seeing Obito. That's how it works. Again, you can say the "truth" and people would buy it especially if you "prove" it. After all, Tobi did train under him.