Intention is very relevant to legal interpretations of "unauthorized access"; both the intentions of the owner, and the intentions of the "intruder". See for example United States v. Auernheimer. There's relatively well-established precedent that when a service tries to safeguard some information, that information is legally protected no matter how technically feeble the attempt at safeguarding it was.
That would make all LLM jailbreaking illegal, not specifically the FBI one.