That's not how it works. You have to kill yourself your best friend, or cause it, and that is what Kakashi did. You don't need to watch them die.Because Obito's emotional reaction to seeing Rin get stabbed caused the transformation.
I mean for crying out loud that was the single event that caused him to lose hope in everything,Kakashi doesn't have the same attachment to Rin for him to unlock MS without Obito's involvement.
Kakashi's only attachment at that time was with Rin, since his father and former best friend died. So yes, technically Rin was his best friend at the time.