I think the trick isn't in making people believe the press is free - the trick is in misleading people about what it means.

The press is mostly free in the US, meaning the government isn't going to explicitly censor or micromanage it. By the same token, the press is also free to do whatever it wants - like, optimize for profits, like a good private sector entity does. Some good ways for an ad-funded news publisher to optimize profits are:

- writing things that get people to read/watch the content (and thus, ads), regardless of whether these things are true, accurate, or appropriate in a civilized society;

- getting paid for delivering more ads, e.g. as sponsored (officially or not) content;

- ensuring ongoing access to freshest news by not burning the sources, particularly government or corporate ones, by e.g. publishing things said sources don't want to see published

This way, a fully free press walks into censorship and bias anyway, of its own volition[0].

Freedom of press is important, but I think we talk too much about ideas and principles, and too little about actual system dynamics in play.

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[0] - Well, as much volition as you can have in a highly competitive industry, where if you don't sacrifice your values, your competitor will, and then you'll run out of money and die.