The relevant question is not whether there is an explicit notice, but whether common sense suggests that you are intentionally making unauthorized accesses - as would be the case with the Google search you mentioned.
If you send a valid HTTP GET to someone's server and they respond with a 200 OK and some content, the access was not unauthorized. The HTTP protocol actually makes authorization an explicit mechanism that may be disabled or loosened at the implementor's leisure.
...though that was interpreting a state law and brought up the fact that the state law has some subtle differences from the federal CFAA (despite very similar wording, quite vague in both cases).
On the other hand, in Craigslist v. 3Taps, a district judge found that simply evading an IP ban, while otherwise accessing entirely (intentionally) public information, counts as unauthorized access under the federal law. And then there's the case of Aaron Swartz.
But anyway, even under the more permissive of the possible standards, your logic is too simplistic. What if I send a HTTP GET like this?
GET /viewarticle.php?title=x%27%20UNION%20ALL%20SELECT%20%2A%20FROM%20%27users HTTP/1.1
It's a perfectly valid and well-formed request according to the HTTP standard, and even valid at the application level, in the sense that you technically can't rule out that an article might exist titled "x' UNION ALL SELECT * FROM 'users", and a correctly written server-side script would interpret the request simply as searching for such an article. But suppose the script isn't correct, and instead of showing an article dumps its user table. Would you say that my access to user data is authorized?
Well, I actually don't know how you'd answer the previous question, but I strongly doubt any court would answer yes. If you say no, then the implication follows that either the difficulty of constructing the dubious request, or perhaps the intent, or something else relatively wishy-washy and subjective can make the difference between authorized and unauthorized. It can't be reduced to some strict technical standard.
If the script is mixing title comments into executed SQL code, then I don't think there is much hope for it. This line of argument allows post facto rationalization for determining unauthorized access. To make a claim that something was unauthorized is to claim that there is some procedure that can determine whether something is authorized or not. That procedure is the thing that should actually be executed when deciding to serve a request. We are talking about cases where the written procedure says the request was authorized, but someone else claims that the actual procedure gives a different result [insert ad-hoc, post-facto rationalization here (ie. not policy)].
This is clearly nonsense, though it may take some time for courts to figure it out.
> This line of argument allows post facto rationalization for determining unauthorized access.
Ah, so the burglar with the bump key is allowed in because the action of the lock determines criminality? "If it opens it's allowed?"
You seem to be making the same fundamental mistake many technical individuals make when they interact with things outside of their knowledge sphere - you're attempting to map a space that is foreign to you into the world you know.
The legal system is not a computer. It does not run on rigid rules That's actually a really good thing: it allows flexibility in considering whether an action is a crime or not.
There's a spectrum to consider. It's clear on one end that a person who searches for "not for release filetype:pdf" may be looking for historical documents, and a person who attempts a SQL injection against a web application has sufficient guilty knowledge and intent.
The legal system does run on rigid rules. Yes, there is no perfect executor (subjectivity will still exist), but the rule of logic still applies. A legal system where you may be convicted of a crime on a whim is not a legal system, it is a farce.
Everyone seems to be ignoring that a 200 OK is explicit authorization, per the protocol. It would be one thing if we were talking about a protocol with no built in authorization primitive, but we aren't. Using HTTP establishes an authorization procedure. Claiming that it may be illegal to receive responses to well-formed requests to the server requires one to make the fundamental mistake of not understanding the technical protocols that are being used to communicate.
The legal system operates on a subset of the logic involved in the technical world. Its ideas and understanding will necessarily lag the reality being created and will be subservient to the logic being established, not adversarial.
Burglary is a crime because it is an intent to commit further crime, not because a door was opened. The difference with an HTTP authorization lock is that the authorizor gets to examine every request and must run their authorization policy on every one. Arguing that the policy that was actually ran was "wrong" is an admission of incompetence.
The analogous situation is where a business posts an "OPEN 24/7" sign by their open front door, but shootgun blasts people who walk through the door.
See also:
https://en.wikipedia.org/wiki/Goatse_Security#AT.26T.2FiPad_...