It sounds like the prison recordings were compulsory, which is a different kettle-of-fish. The key phrase "if they share" implies voluntary and deliberate action, and is not much of an oversimplification imo.
> What matters is that the parties intended and expected communications to be privileged.
I would contend that your summary, not theirs, is a oversimplification. Jurisdictions will obviously differ, but privilege does not attach merely because of the intent and beliefs of the lawyer and client.
Well, I try to avoid the R word. The actual legal term would be reasonable intention. Literal expressed intention. ie putting an A-C warning on every email, won't be enough on its own.
IMHO we should just assume the R word before every verb in every legal discussion. That is how reality works. These are not spells. If I express that I intend something to be private, then announce it using a megaphone at a basketball game, my intention is no longer reasonable regardless of what magic words I have thrown into my communication. Act like an idiot and a court will treat you like an idiot.
> What matters is that the parties intended and expected communications to be privileged.
I would contend that your summary, not theirs, is a oversimplification. Jurisdictions will obviously differ, but privilege does not attach merely because of the intent and beliefs of the lawyer and client.