itachi killed shisui he fully admitted to that.I think you get MS from realizing and accepting a loss of a loved one.
Itachi did not kill Shiusi but has MS
Sasuke did not kill Itachi but has MS
So Kakashi probably accepted that Obito's death wasn't his fault and accepted it
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itachi said he helped shisui dispose of his body which means he help kill shisui even though shisui told him too. itachi still killed him. they both didnt goto the meeting. and itachi killed him with shisui permission and itachi disposed of his body keeping his MS. also shisui did write that note that they found