Hi John,
Thanks for your update.
Since there are many differences in Outlook 2011 and Outlook 2010. To make sure the issue is not caused by the network settings, please let a user use another network environment to test it.
Moreover, as you said:"another user claims she's getting some sort of message saying her message has been "rerouted" ", based on my experience, this issue often happens after the Outlook client connected to an Exchange server.
So, could you please let the user provide the screenshot for further research.
Regards,
Jerry Cen