I've been rereading the chapter where Obito saw Kakashi kill Rin and go nuts. Anyhow, it seems the whole point of the mist ninja's mission was to capture Rin. Kakashi killed her for no apparent reason, and the ninja seemed determined to retrieve her body even after she was killed, so it can't be information.
I was thinking the whole thing might have been engineered by Madara to turn Obito to his side, but Obito did see from Kakashi's eye for a while so I don't think that can be it (unless Madara's influence runs really deep). Also there's that tiny matter of Obito controlling yagura for a while after that and starting the bloody mist regime. I'm stumped really, there must be more to that story than has been revealed yet. the only logical conclusion is that rin had some special ability, but if so she displayed none of it so far