If someone reports a PM in the forum, then the admins (not the moderators) are able to read the PM, as far as I know. I wonder, how that works technically? Do the admins receive a copy of the PM, which is reported?
I can't comment on Talk, but by default the Simple Machines software that drives this forum does not allow Admins to read any PMs not intended for them unless it is reported by the recipient to them. They believe strongly in individual privacy. As with any database driven platform that doesn't mean someone with the right technical skills and access couldn't access the database. As Simple Machines say; For this reason, it is advised to not send personal messages that contain private information that you do not wish for anyone else to read.
So the admin would just get an email report which would contain the reported message and who had posted it so that they can respond and resolve the reported issue. As mentioned previously, we Mods don't receive PM reports.
Hope this is helpful
As far as I know, this is pretty much how it works in most, perhaps all, the well-known internet (discussion) forum platforms (e.g. covered in Wikipedia's Comparison of Internet forum software), albeit with minor variations.
The Zooniverse's Talk - both v1 (as still used by Planet Hunters, for example) and v2 (Galaxy Zoo, and more) - is, in the language of the WP article, proprietary. And as regards its Messages, it differs considerably; for example, there's only one recipient (so no Bcc: ability either), no ability to forward, and as zutopian noted, you can't report a Message either. Also, quite unlike any of those in the WP article, details of how Talk's Messages work are unknowable (unless you are a Zooniverse Developer)1.
ETA: and, as Hanny noted, you can't delete Messages (you can certainly delete PMs in commonly-used internet forum platforms).
1 Though with a lot of patience, you could treat it as a black box, observe the behavior and deduce likely rules (built in to the code). You could also visit GitHub.