Meeting Requests marked as Private

One user (A) sent what was supposed to be a confidential meeting request to
(B)and realized she didn't mark it as Private. She went into the scheduled
meeting, marked it Private and sent an update, but it didn't update the other
attendee's (B) meeting as Private. Other users (C) could see the details of
the meeting request when viewing the attendee's (B) shared calendar. Is this
normal behavior or should the update have updated the Private setting.

I tested this by doing the same thing from my calendar, created a meeting
request from my calendar, invited a couple test users, sent an update with it
marked Private and sure enough it didn't mark the meeting as private after
the users received and accepted the update.

Does anyone know the proper behavior and why this might not be updating?
Thanks.