I think the larger point is that private messages are visible to instance admins.
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Yes. And I think saying "messages in Lemmy are not End-to-End encrypted" is clearer communication than "messages in Lemmy are not secure".
Messages between two people are not exposed via public APIs, but they can be accessed by admins of 1-2 servers (depending on whether you're sending these messages to someone on a different server).
Element fixes Lemmy's message content exposure problem, but none of the metadata problems (who is communicating with whom, when, how often, etc, are all still available to those 1-2 sets of server admins).
I agree. That's why I propose to clarify the wording.
Based on the comments so far, maybe something like this makes sense:
Warning: Private messages in Lemmy are not End-to-End encrypted, so the respective instance owners are technically able to read them. Please use a platform with E2E encryption for private messaging. Lemmy recommends Element.io and XMPP.