I suppose Trump's statement plays into his fake news bit. All presidents have tried to control the media to a certain extent. Not overtly as Trump seems to be doing. But this goes back to his war with the media shortly after he announced his bid for the presidency back in 2015. We know Trump and the MSM are in the midst of a feud. Most people recognize this and probably pay little attention to it by now. Trump isn't subtle in his attempt to control or at least degrade the media.
This feud, Trump has brought out into the open. Now this game has been going on for a long time that predates Trump. Republicans complained a whole lot about the MSM being on Obama's side and not treating him like they did G.W. Bush. Let's face it, even without Trump public trust in our news reporting media has been on a decline. Before Trump even took office. I think it is because the press, the media has taken sides in our political battles instead of just reporting on those political battles. How many American's are going to jump up like you did over this "Don't believe." They already don't trust the media to report the news fully, fairly and accurately.
Take a look at this, public trust in news reporting, the media was at its highest in 1976 at 72%. That dropped to 55% during Bill Clinton, further trust eroded during G.W. Bush down to 45% by the time Obama took office and now has fallen to 32% in 2016 the last year of Obama.
https://news.gallup.com/poll/195542/americans-trust-mass-media-sinks-new-low.aspx
You can see the break down by party further down in the article. Mistrust is already out there by the time Trump took office. Most folks ignore this fake news and don't believe stuff as pure propaganda. Being trust in the media wasn't there when Trump entered office, he's winning his war with the media because the people distrust the media. 46% of all Americans think the media makes up stories about Trump to degrade him and make him look bad. that it's the media that is dishonest.
Poll: 46 percent think media make up stories about Trump
https://www.politico.com/story/2017/10/18/trump-media-fake-news-poll-243884
If the media hadn't taken sides in our political battles, long before Trump. Perhaps more Americans might trust them and be shocked like you. But the media lost a lot of their credence and respect a long time for Trump. Trump is just using that loss of credibility to his advantage.
When only 32% Americans trusted the media prior to Trump, they're apt to start now whether the media is right or wrong. The media has done this to themselves, Trump is just very good at playing to what the media had done to themselves.