I think you misread what I said above @graham, I specifically said I was not talking about SF, and also said pointedly other places, in other words at least one other forum I have been on.
However what has been said since your post now confirms me in my view that Private Messages are not private, and thus I maintain my dislike and minimal use of them.
And to @kirsteastevenson , as a confirmed non techie yes, I am naive and daft, as you put it. 
In all honesty I was thinking of some of my peers who have been brought up in the internet age and really should know better! Without wanting to sound patronising because I know we have some very smart, very tech savvy people here, I think it’s only natural that people who have not been brought up with this stuff at the centre of their world may be less savvy, that’s not naive and daft, that’s just natural, it was the people my age (well, younger really) who really should know better as they have had the internet and mobile phones and tech as a part of their everyday life since birth and use it all day every day, that I was thinking of there.
Kirstea’s point is that it s too easy on Discourse and some people might not know that.
My expectation would be that site owner and authorised IT could see PM’s if there is a reason to. But not that quite large categories of user with some admin capability awarded to them, might also be able to gain access relatively easily. This is kirstea’s concern.
let’s put this into perspective…
There are at least 13k+ members on SF each of them capable of sending a PM and if you think that James has enough time on his hands as Site Admin to monitor each and every one… then think again 
AFAIK James, Cat and billybutcher all have jobs to keep them occupied and daily lives to lead and cope with so any risks of PM’s being compromised as a matter of routine is highly unlikely…
Besides all that… if you know someone on the site well enough to transmit personal or compromising stuff to, you probably also know their private email address which would a more prudent method of communication surely.
Just to set your paranoid mind to rest (albeit somewhat belatedly!) it definitely wasn’t you, @Pamela_Shields !