I do wonder what happened to the couple and feel sorry for that female. Personally, I don't think this is a real iPhone bug, however, I did notice something very similar can be done with Thunderbird (my favourite mail client). Similar in the sense of getting a mail in your Sent folder or (Inbox itself) that you never sent!
Here's what I did. I have two mail accounts set up on TBird, Gmail and my work email. Now, I select some random mail from one of the accounts (say gmail) and drag-drop it inside my work email's inbox. Now, my gmail (webmail) account shows the same mail as if it was sent to the account. Of course, the 'To' address field hasn't been modified, but it looks identical to case of being in 'Bcc' when the mail was sent.
I don't think this feature can affect businesses (though it is quite easy to modify the 'To' etc fields using some software) however, it can be used as jokes on your friends or if you want to cut out someone from your life....
Coming back to the troubled lady's case, I have shown that these things can be made to happen but I do not know what the chances of all these happening on its own are. But its not impossible; improbable but not impossible.
Update: The husband seems to have gone as far as creating a new account on Apple Discussions to reply to his 'wife' that he (ie some 3rd person) has also experienced similar problems :P