Newspapers could always publish anything by just saying "I found it on the internet". Which is obviously not the case. The free speech and free press clauses protect public media as much as individual persons but what you say on social media will still be used against you.
And talking about freedom of press, France doesn't look that bad at all. [0]
humanrebar wrote that if it had hypothetically occurred in the US, it would "push against the First Amendment". You quoted that phrase and replied that it "isn't a freedom of speech issue", which I interpreted as disputing the claim that it would hypothetically push against the First Amendment. I replied in that context.
Whether it violates freedom of speech in a more abstract sense is, of course, subjective. I think that requiring the press to do some degree of due diligence is not unreasonable, but I also think there are advantages to the US's more deferential approach.
As for the Press Freedom Index, I'm under no illusion that the US is perfect in that regard.