IANAL either, but I don't think it's even that complex. You can have all kinds of legally-compelled data requests come up in a subpoena or in discovery. Even if the models were completely self-hosted on the owner's own computer, the opposing side could ask the court to make you hand over those logs, in the same way they could ask for a copy of your journal. While the 5th amendment right to not incriminate yourself still holds, I think a self-owned AI would be just as subject to a subpoena as your diary or calendar or whatever else. And in no case could I imagine it would get the extra protections of attorney-client privilege.