You might be interested to know that the “illegality” depends on the intent. If I rest on your unlocked door handle, it opens, I enter, it’s an accident.

Sorry, what? In this scenario are you claiming that you accidentally fell inside the restricted area because you were leaning on the door? Or are you claiming that you accidentally opened the door and then walked through intentionally? In the former case, you are guilty of breaking and entering in most US jurisdictions if you don’t promptly get out. Any sane court would likely agree an accidental trespass is probably not a criminal act, but it’s not an accident if you stay. In the latter case, you’re clearly trespassing illegally.

Also this has gotten pretty far away from the web scraping scenario. There’s no door accidentally opening here.

Oops, I just accidentally fell into every website. Don't know how that happened ...