Third Update: somehow during the latest update (again, not sure whether this is a WP update or a VFB update), the "Notification" settings were lost. What was in fact happening was that the "Notification" option was still turned on, but the reply-to address and other required fields were missing. This is odd, because you cannot turn Notifications on and submit the changes if the required fields are blank. It makes me wonder whether the Options field names were changed during the last update?
At any rate, this explains the reason the emails were being sent: the email to the admin mailbox were going through, but the error was being generated by the second email (the notification email).
The solution: check to see whether you have Notifications turned on. If you do, be sure the "reply-to" address is filled in.