Update, It seems that this was caused by overloaded servers.
On Tuesday 12/20, a portion of NTT Docomo SP Mode Mail customers had their mail address swapped randomly with other users. This incorrect address was displayed to recipients of mail sent by affected customers. Replies were also directed to the incorrect mail addresses. Thus far, NTT Docomo has received 103 complaints of incorrectly set addresses. The reason for the problem is under investigation.
To verify your address, from mail settings go to other (その他) and then address. If the wrong address is displayed, reboot your phone to restore the proper address.
NTT Docomo has partially suspended SP Mode services in response. See the announcement for the fully list of stopped services, but it is probably a bunch of stuff that no one reading this blog uses anyway.
(I bet when Docomo implemented their carrier mail system 10 years ago, the way they did it probably seemed like a good idea. If you looked at the specification today, you'd probably ask WTF were they thinking.)