This is an excellent point, and worth stressing because it goes against the average Civ player's intuition. My last game is a good example.
Playing England on Emperor, I drew Austria, Brazil and (on the other side of the continent) Assyria as my neighbors. We all had DOF's, and I had two units and ZERO ships by the time cruisers were available. Yet I was right up there in the tech race, largely because I converted all my neighbors to my religion before they had one for themselves. (Sainthood in these conditions is amazing.)
I also controlled the WC. When the points leader Incans gave me a DOW for blocking their progress in the WC, I built up a fleet of four SOTL-upgraded cruisers and one ironclad, while killing the stray units the far-off Incans sent over. Then I sailed over the top and attacked his capital -- took it -- and got a peace treaty that very turn.
The Incans fell to third in the standings... but I began to lose control of the game to Austria. Despite one successful decolonization, Austria, which had expanded easily in the early and mid-game, became too rich to stop its CS alliances and marriages. I would have needed to compete directly for a Diplo victory, but had decided prior to starting that I was going for Science. (And competing for a diplo would have been tough, given my much smaller size.)
Not expanding in a second wave until it was too little and too late made me fall behind in the Wonder race, after having led it. Austria could probably have won a Science race eventually. But they easily beat me in the first UN vote for the win.
Looking back, fighting them in the WC wasn't going to be enough. (Maybe sanctions, but I doubt it.) What I need to do at some point is attack them the way I did the Incans. I didn't, because of the diplo consequences: we were allies, and both Freedom. But in retrospect, that was my only chance (playing a restricted game where I only had one, difficult VC).