It may be a very legitimate fear, depending on your audience. The best way to get ahead of that if you don’t want to switch the systems off is to use watched words or AI triaging, and to have very clearly documented policies explaining that admins have access to all private messages and chats for moderation and safety reasons.
The illegal harm and how you deal with it is the same whether in a public post or a private one, but you are correct that you greatly reduce the risk of harm by closing private channels.