I think your understanding is very wrong. The closest clause I can see in the link to posting guidelines at FR says the following:
# Don't violate poster privacy - Don't reveal online another poster's phone number, address, or other information that the person hasn't already made public for everyone on Free Republic. If you are asked for a friend's email address, the best advice usually is to forward the request to the friend. He or she can then decide whether to respond.
Now it seems pretty clear to me from the above that one should not post private e-mail. Which only makes sense, if one wanted all to read it, one would just post it on a thread. So unless one receives permission to do so, one should not do that.
Now, as I said, what's done is done, and this is not an attack on you. but we should not do this again.
If the closest clause in the FR forum rules you can find isn't all that close, you're wrong.
Now it seems pretty clear to me from the above that one should not post private e-mail.
"... Addresses."
That's what it says. Don't post people's private email addresses without permission.
Now, if we're buddies and--never mind the medium--you confide something to me that could be harmful to you, only to have me blab it all over town, I've betrayed a confidence.
If my dog dies, and you send me note gloating that you poisoned him, only to have me show said note to the police and all the neighbors, you were indiscreet.