I am just taking the error message for its word. I wouldn’t know if you get the error while playing singleplayer offline, would be strange considering how specific the message is but it wouldn’t be impossible since bugs do happen.
And you can be connected to a server outside mutliplayer. There’re leaderboards, optional co-op, general stat tracking and much more in recent AAA games (gta 5 for example, you can see your story progression on the website).
Nothing anyone here can do to fix issues not related to Infinity.