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.