My theory is based off the assumption another poster made (that when Obito smashed in one of the Hidden Mists' Anbu Masks, the headband behind it did not fit the profile of a Hidden Mist Head band, but rather, of a Hidden Leaf symbol.)
Off this assumption, I shall continue.
The Root wanted Kakashi to obtain a higher form of the Sharingan, so created a situation where Kakashi was led to believe that killing Rin would be for the greater good of the village, thus awakening the 3 tomed Sharingan (and the Mangekyo) due to the emotional stress that usually awakes such power.
I have a theory along the lines of yours but rather, that Madara sent Obito out to see Kakashi kill Rin so he would activate a higher Sharingan. The head band is a good point it does ook like the Konoha triangle showing. For anyone curious it's chapter 605 "Hell" page 14ish
First, when Obito leaves to "save" Rin he says he won't be back and thanks him, Madara tells him he will and he'll thank him sincerely when he does. Why would he thank him sincerely? Because Madara led him where he needed to go to unlock more of the sharingan.
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IDK why my pic link won't work but this is chp. 604 pg 6ish
Second, When one of the mist ninja attack Obito where rin dies he yells "Don't underestimate the village of the
bloody mist" The only time I remember this name mentioned was by outsiders describing the village in the mist in an ancient time. Madara more than likely knew about The village of the bloody mist legacy, and this is his slip in the genjutsu to give readers foresight. If the bloody mist moniker was used by outsiders and not mist ninja then someone must have orchestrated the "attack" on rin.
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This is chp 605 pg 5ish
People may argue "but why Kakashi's eye evolved then too" Well of course the eyes are still the same set of eyes they were when they were in one head. If one evolves the other will as well.
I think the whole thing Obito saw was a genjutsu on him and Kakashi never killed Rin, because nothing else would expain why originally it was said "Kakashi you LET RIN DIE" now it's "Kakashi YOU KILLED RIN" if it turns out Kishi just did it to keep us in the dark until the time was right I'm good with that but something doesn't sit right as it is now.