I don't see what wealth and influence have to do with it. I think that if Website X is owned by a resident of, operated within the borders of, and complies with the laws of Country A, Country B should not try to bully the operator into changing the site. They can order domestic ISPs to block it if they want, or they can not do that if their citizens value Internet freedom.

If the site doesn't comply with the laws of Country A, or if the website operator hides so nobody can figure out which country is Country A, then it's an entirely different story.