UPDATE:
It appears that I inadvertently sent my message to the other member via email, not PM. She had the option to receive emails checked. I was thinking I was sending a PM, but it was actually a communication via email.
Still, there's nothing that tells you that sending an email automatically discloses your email address. I would assume that nothing but my user name would appear, and that any reply via email would have to go through SR.
I've updated the admin staff, so they don't go looking in the wrong places. I honestly thought I had sent a PM. Seems like there should, at the very least, be some kind of warning that sending a message via email results in disclosure of your own email address so the person can reply directly to you. It's still troublesome.