Thinking is NOT independent when such thinking consists of actively looking for sources that confirm your biases. Something that is facilitated by the algorithm that handle social media. That is the problem. A problem I've and I bet you have encountered on numerous occasions.
True independent thinking consists of carefully selecting sources, preferably primary sources. Carefully reading and comprehending these sources and coming to your own conclusion based on that information. While at the same time being self-aware enough to understand and combat the human tendency to suffer from conformation bias.
It is time consuming, takes quite a lot of effort, and can be extremely uncomfortable when the opinions reached by looking at the facts aren't the same as what your biases say.
Since very few people bother, understandingly so, they rely on others to do that work for you.
Herein lies the problem and the reason for Gore's comments. The fourth estate has certain rules of conduct. Policed by themselves and (not always successfully) adhered too. On the other hand, a large part of the world instead chooses to just accept whatever information that agrees with their preconceived notions, no matter the source, including sources that have absolutely no compunction to be truthful. And because they feel that information is being withheld from them by the MSM, they become distrustful of that media, pushing them deeper into their echo chamber in a constant feedback loop.
To you, information you find on some niche blog is considered reliable precisely because it comes from some niche source and not the MSM, and because you take the time and effort to keep on looking until you find that information you are an "independent thinker."
I'm willing to prove it too. Take any topic. Differentiate between what you think and know. And only accept those things that you can prove by primary sources and discuss it with me, while I do the same. See where it leads.