Above and Below Display Arrangement in El Capitan
I think I may have just solved it.  I have two accounts on this Mac, my Admin account and my daily use account.  The admin account didn't have the same screen orientation as the the daily use account, and on the login screen the admin account was listed first.  I suspect that when no accounts are logged in that OS X grabs the screen configuration of the first account that it finds - which happened to be the admin account in my case.