Is putting random shit at the end of a URL really illegal?
We're at a gaping chasm of misunderstanding here. Tech people see websites as things to be used and toyed with. Non-tech people see websites as things that have terms of service that are supposed to legally restrict what you can do. "YOU MUST NOT ACCESS THIS WEBSITE IN ANY AUTOMATED FASHION WHATSOEVER."
They argue on a basis resembling: "You wouldn't break into the admissions office and steal the list of accepted candidates, would you?" We counter-argue that it's like knowing a person who can't lie to you. If you ask them for the result, they give you the result. Is it illegal to ask for an answer if they don't even hesitate to give it to you?
Consider banks not having vaults and instead leaving their money sitting out in the open. It would be easy and tempting to swipe some. Doing so may be "wrong" technically, but by the availability and lack of security, one can presume the banks are aware of the risks and can tolerate some shrink.
I would argue it's not wrong if they put no security in place, it's in a public place, and no person is denied a resource by your act of accessing the public resource with no security.
Like a bank whose tellers (a gatekeeping mechanism) will give you however much money you ask for as long as you end your sentence with "swordfish" - they just don't tell anyone about swordfish.
I also recall a case where someone just removed one or two directories from a path and found an unprotected virtual listing but they said it was unauthorized because he had been sent a 403 at some point.
The intent to break the law, the intent to commit terrorist acts, can indeed be illegal. The intent, however, cannot be contained by "random characters," as you put it. The law does seek to ensure that people can live without fear of attack, but the act of mentioning terrorism or mentioning terrorist acts is certainly not illegal. And this is specifically what you said: you said that the random characters which make up a terror plan or worse are illegal.