Yeah, well, didn't turn out to be true, did it? For the few hundred years after he said that, the only country that might fit Jefferson's hopeful criteria was Liberia -- and that was founded by people who had to leave America to be free. Meanwhile Americans wiped out the Indians and got started on the rest of the non-white planet, like the Philippines, except fortunately there wasn't too much left by the time they caught up with the Europeans on empire-building. For the century and a half after Jefferson's statement, the world aped the culture of the British (and the Germans and the French -- but of the 3, only the British were really a free people). Then in the twentieth century, as America grew rich and Europe lost its wealth -- surprise -- the world started aping American culture instead. And in all the intervening centuries, the only real freedom that's been spread in the world has been by 1. Empire and decolonisation (the British and French colonial empires), 2. bloody, murderous, foreign war (Western Europe), and 3. economic liberalisation (Eastern Europe and some of Latin America). Latin America is kind of a special case: a combination of revolution, foreign intervention, and unstable democracies dependent on prosperity. (You might say the same about most of Africa.)
No, you'd be shocked at just how much foreign entertainment people can pick up and have their society's worldview untouched. I've seen it first-hand. The only way to get freedom and democracy to stick somewhere seems to me to have it established in a prosperous society for several generations, and keep some level of prosperity. Establishing it can be very hard: apart from war and empire, only gradual economic boosting and intervention seems to work, but it's so easy to get wrong. The EU might prove a good model of doing it right.