Discrepancy in Outlook Desktop and OWA for Shared Mailboxes

If an incoming email is flagged with "Sensitivity: Private" then due to how Microsoft define permissions these emails won't be visible to all users in a shared mailbox.

If you are not the owner of the mailbox then you need to do this via OWA.
Select Open another mailbox and then open the shared mailbox > go to Calendar > right click on the calendar in the left folder menu and select sharing permissions.

You need to add each user individually, selecting Delegate from the drop-down and checking the box labelled Let delegate view private events. These users will now be able to view the emails marked as "Private".