So I think you'll find that the better-constructed laws require overt acts that inform us about motive in many (but not all) cases, rather than mere inferences about motive. Though I certainly agree that there are reasonable facts which one can use to infer mens rea from. Good intent can also be inferred--that's why I specified a safe harbor for people who were trying to simply do the right thing and report a bug they'd found. Someone who reports a problem to the site owners in good faith is simply not someone I think we should be hitting with criminal penalties in general, though this might be weighed against other things like attempts to ransom the bug or sending DROP DATABASE injections and whatnot which could wipe out any inference of good intent.
That said, I've always said this was my view of how the law ought to work. Implicit in that is that the law does not, in fact, work that way, so I honestly can't disagree with you here--the law certainly doesn't work my way, and this is all my own thinking on how it ought to work in my own view. So inasmuch as you're saying the law doesn't work this way, I completely agree.
There has to be 1) believable intent to 2) commit an actual crime.
Your reasoning is circular without that - "he had bad intent so whatever he was doing was illegal which is how we can say his intent was bad rather than simply unsavory, etc."
There's no valid precedent for simply requesting a document being illegal, nor ultimately a security benefit from it being so.
If they actually do that or take steps that would make a reasonable person conclude that they actually were on their way to do that before they were caught? Then yes, hammer away.
I'm more concerned with their being a brighter line for what is and isn't unauthorized access and a safe harbor so people can't hammer anyone who simply makes them look bad by pointing out that their fly is open.
If you can fit facts of some old case to show that they were guilty in a principled way, I won't argue. I may or may not agree with the specific reading of the facts, but at least I would find that to be a principled disagreement.
My point in this exercise is to shift things from an exercise in how people feel about some particular intrusion or a person's motives which are things not likely to reach broad consensus to an exercise where we debate the specific facts of the case which reasonable people should be able to agree upon given enough information, no matter how they feel about the parties of any particular case.