Do you actually watch Fox News? Were you aware that it was Fox News that first called the election for Biden? Were you aware that Fox News virtually always provides someone to give an opposite point of view to that of show's host on political matters? Something I don't see on other media outlets.
To me media trust is based on free speech and free press. CNN, MSNBC, the NYT, and Washington Post are the real media outlets that have violated the integrity and trust of the American people. Not because they are progressive liberal leaning media outlets, but because they have failed in their most important responsibility and that would be making sure the American people are fully informed on all points of view regarding the political issues of the day.
It is asking to much of media outlets to "report just the news" given most are now controlled by billionaires that want to use their platforms to spread their point of view, but it is not to much to ask media to provide at least some responsible reporting on the "other side's" point of view.
Jefferson said Freedom of the Press and Freedom of Speech were essential in order to insure that a democracy could function. With different points of views competing in the marketplace of ideas democracy was doomed. Private sector censorship can happen in two ways and be as bad for a democracy as government censorship.
1) the private sector can suppress speech by denying access to the means of "thought" distribution which historically has been the media and in recent years extends to social networks.
2) alternatively, the media can simply ignore that other points of view exist and in extreme cases resort to name calling and other means to "cancel" those opposing viewpoints.
So now let me offer you this challenge... watch Fox News vs CNN for one week. Write down how often Fox News includes people with opposing viewpoints on political matters and compare that with CNN. Then decide which media outlet has violated the integrity and trust of the American people by failing to inform them of opposing political thoughts that are so critical for a democracy to function. Good ideas can only emerge if they compete with other ideas...