Both are true. It's very hard to control information exchange to such a degree that determined persons cannot find a way to exchange information. But your average citizen doesn't have any reason to be determined - they consume information from mainstream media, and so long as it isn't obviously off, they aren't going to double-check every bit of it.

Thus, over time, you can gradually create a bubble, lie by lie. I remember the early 00s - freedom of press wasn't gone overnight, they went after the more popular stuff first, and then gradually it became more and more marginalized, with the last vestiges being swiped away only now. But with every independent TV channel or newspaper erased, more and more people ended up in the bubble.