Scaredypants has the most plausible explanation.
Apparently, ahem, there is software that allows you to spoof the "from" email address. So I could, ahem, if I had such software send an email to the Queen offering her sexual pleasures from say, Bill Clinton (if I knew both of their addresses).
It's quite easy, er, apparently.
The items will never appear in your sent items folder as they were never sent by you. To the recipient though these spoofed emails are undeterminable from the real thing.
There is substantial fun to be had with such software, but remember people, it is VERY illegal…….