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A while back, I had a user call in, telling me that all meeting invitations she received for some reason also showed up in the inboxes of a couple of shared mailboxes. I logged in to her computer remotely, and started poking about. I tried a number of fixes, including deleting her profile and recreating it, at which point i stumbled across a reference to delegates.
On a hunch, I went to File > Info > Account Settings > Delegate Access, and there it was; It turned out that she had set up her email account to grant the shared mailboxes delegate permission to her own inbox, like so:
Once we removed those permissions, everything was back to how it should be.