Looks like I might have to take this thread seriously.
Ok then, listen closely. You say that Obito was the true owner of the Sharingan and therefore his vision could not be see by a "borrower", that is Kakashi.
In other words, you try to say that vision from Kakashi went to Obito but vision of Obito didn't go to Kakashi. Remember this well, since this is the crucial part.
You say that this "shared vision" is a proof of Kakashi's MS being awakaned by Obito.
If Obito awakened his own MS, there is NO REASON that it should go to Kakashi as well, since this connection is ONE SIDED ONLY - from Kakashi to Obito, NOT the other way around, as seen with the vision.
In other words, if anything, it's KAKASHI that awakened MS which then went to Obito, just like the vision.
End of story.
Congratulations, you just made me prove you that it's totally the opposite of what you were thinking. Are you happy now?