Do any of us really trust our peers?
Personally I think jury duty should just be mandatory (with the only exceptions being extreme circumstances) because it being so easy to get out of creates a major bias in the set of people actually doing jury duty.
Comparable activity: let's ride around the neighborhood and see who hides a key under a rock. Then let ourselves in and look around.
Imagine if your Doctor left your personal medical records lying on the ground in front of their office...
If we're going to try to force physical analogies to represent the digital, I would say it's more like every store, house, and public building looks exactly the same and you don't know if the door is locked or what's inside it until you try to open it.
You have a person cruising for keys to a house and a person cruising for keys to databases. They own neither.
Accessing a URL is like walking around the neighborhood looking from the street. Trying different URLs is like peering into windows. Trying the door is like testing default credentials.
To make something a crime, you need to prove some kind of loss as well as intent. If there's no intent, it's likely a civil case to get restitution (e.g. you won't arrested for breaking something in a store accidentally). Likewise, you could get arrested for intent without loss (e.g. tried to break something in a store, but failed).
IMO, it should only be illegal if there's intent to harm. Likewise, if you accidentally harm something without intent (e.g. accidentally DOS a server), you should be expected to make restitution. Both need to be proven in a court of law, criminal if there's intent, civil if there isn't, and if there's no harm or intent, there's no crime.
Here's an analogy I think is closer: I ask you for all your personal documents and bank account numbers. You promptly give them to me with no questions asked. Was I accessing private property improperly? If you refused and demanded I identify myself as someone authorized to have access, and then I forcibly took them from you anyway, that would be criminal.
Web addresses aren't property, I think that's the wrong analogy. The web is made of requests and responses, and you don't know what response you'll get until you make the request.