Short form: I've always taken it as an inviolate rule that you don't forward private email. (And that private email, in another absolute, includes mail to a mailing list, unless that list has a public archive.) I have always taken forwarding here to mean quoting at all. There are some circumstances where it's okay to summarize such email, but not to paraphrase it. All of which boil down to when your purpose is benign and you're confident the sender wouldn't object to your doing so.
But under no circumstances, under the netiquette I was taught, is it alright to quote private email without the sender's explicit permission.
I suspect that the modern take on this is that I need to relax. That holding rigidly to that rule, while not as odd as, say, insisting on calling my co-workers Mr or Ms Lastname rather than by their first names would be, is nevertheless passé, and no-one would take exception to my using my judgment in such a matter. (They might question my judgment, but not assert that there are no circumstances in which it would have been acceptable.)
I was going to follow the above with the "long" form, for anyone interested. I started writing the above when I found myself 150 words into the first draft and still hadn't gotten to the question. It's now taken me 250 words to ask it directly. I'll spare you the prologue.