Meeting Requests Don't Show Up in Google Apps Mail

We use Google Apps for both our corporate mail and calendaring. I've observed that while I am occasionally sent meeting requests -- both from people inside our company (and hence on Google Apps as well) and outside of it -- I have never seen even one actual meeting request mail. Instead, I just happen to notice that a meeting has magically appeared on my calendar.

In addition, it appears that the meetings haven't actually been accepted. If I set "Automatically add invitations to my calendar" to "Yes, but don't send event reminders unless I have responded "Yes" or "Maybe"" then they disappear from my calendar. But the meeting request is nowhere to be found regardless of the setting.

I'm not set up as a resource (like a conference room) so there's no auto-accept option to disable. Very perplexing.

I access my mail through web, Outlook and iPhone and can't find any Outlook or iPhone settings that might have caused this. Or have I missed something?