> Likewise, users on the internet have no "right" to access anything
Yes, they have a right to block you, but that doesn't imply that a terms of service which prohibits automated access is legally enforceable. A TOS is not a contract so you can't put whatever you want in there and expect a court to honor it. To my knowledge US courts have not decided ohitsdom's question, but I could be wrong.
However, if the site makes an attempt to block you from automatic access (even an IP block) and you circumvent it, you're in violation of the Computer Fraud and Abuse Act. See Craigslist v. 3Taps. (disclaimer: I'm not a lawyer)
I'm not sure sites can sue journalists for investigating them. Or rather, I don't think they will win. In the U.S., anyone can file a suit against anyone, merited or not, of course. Sometimes in cases like this defendents can get damages from plaintifs under anti-SLAPP laws. But it's still gonna be a long road to get there, if your opponent has the bucks for it and you don't.
They don't need a specific "right" to control their servers. Likewise, users on the internet have no "right" to access anything.