Working in computer security, I've learned to be *real fucking careful* about this law and have heard of it being interpreted *very broadly.* If a client of mine described a system to circumvent access restrictions like this I would fire them. But assuming I didn't fire them, I would
1) tell them to shut it down immediately
2) tell them to talk to a lawyer.
LLMs, as a class of user, are clearly not authorized to access the information. By circumventing access controls, they have "knowingly accessed a computer without authorization." Those access restrictions exist to protect against various damages, including bandwidth use and "intellectual property theft" (another concept I'm not a fan of, but anyway). By violating those restrictions they could open themselves up to legal liability.
Now, IANAL. My job is to describe risk. That's a sufficient risk. It actually doesn't even matter if you'd win the case in the end, a lot of people just can't afford to fight.
But, in this case, it tends to be powerful people, for whom the law does not apply, abusing people who neither have the protection of the law nor the money to just ruin someone's life with a flood of lawyers.
https://www.law.cornell.edu/uscode/text/18/1030