I thought it was very obvious.
Kakashi developed the MS by grieving the loss of his loved ones. Most likely Obito, it could also be the combined grief of losing Obito, Rin, Minato, and his Father.
It has never been proven that you have to kill your friend in order to attain MS.
Itachi didn't kill anyone close to him to unlock MS, he only lied and said he did.
Itachi obviously gained the MS from the death of Shisui and the countless other deaths he's witnessed as a child.
Sasuke did not attain MS from killing someone close. He got it from Itachi or from feeling the pain of losing his beloved brother.
Madara nor Izuna weren't rumored to have killed someone close to attain MS either.
Shisui also did not kill anyone close to attain the MS as far as we know.
All of that, Killing a loved one BS was just a lie by Itachi so that he could make Sasuke strive for the power to kill him, so that Itachi could seal his jutsu into Sasuke making Sasuke think he unlocked it on his own IMO.