Have I committed a crime? There were no doors, no locks, no signs to tell me that this area was restricted. Just because it wasn't on the map and may have not had a clearly marked entrance, doesn't mean that I should have known it was a restricted area.
Most criminal tresspass laws require at least clear signage or a previous communication, and even then, the area has to be clearly defined. You can't just wave your hand and say 'if you go over there, you're tresspassing'
There are some large(20,000+ acres) areas near me that are used as ATV playgrounds. The ATV riders are not authorized to be there, and the land owners have taken some steps to put up signs. They are not consistent or ubiquitious, and the properly lines are not clearly marked or identified. Being that the area is not surveyed, law enforcement is very reluctant to charge anyone with criminal tresspass because they can't even tell themselves where the legal property lines are.
Imagine trying to convince a jury beyond a reasonable doubt?
People on here talk all the time about how their digital possessions are just as important as their physical possessions (if not more-so). Given that it seems perfectly reasonable to have the same cultural norms about exploring digital spaces as physical ones.
If I broadcast a request for an IPv4 address and your DHCP server proffers an IPv4 address that I can use for the next 15min, the address of a nameserver, and the address of a router that will forward packets to the global internet, I can reasonably conclude that you intended to allow me to exchange packets on your LAN and at least attempt to use your gateway to interact with the internet. On the other hand, depending on the situation, a "403 Forbidden" could reasonably be interpreted as a request to not send that type of HTTP request anymore.
The protocol isn't the only place to look for intent, but it absolutely does express intent in some situations.
If the owners don't want something public, it's trivial to lock it down--they might as well freak out when somebody uses the wrong door to enter the front of their shop.
The protocol is relevant, because it conveys information. Just as unlocked doors generally indicate permission to access, unsecured HTTP generally indicates the same. But the protocol is only one piece of the puzzle. It is not dispositive. It does not conclusively decide rights and responsibilities. If a reasonable human would discern that the protocol allowing access was probably the result of a mistake rather than intent on the part of the property owner, that is what matters.
Making a mistake doesn't relieve one of legal protection from trespass (physical or digital).