Better headline: half of Americans don't know that (many) news organizations deliberately mislead them.
Not in the US, but I usually see a lot of people saying don't trust the news but it's also not as if they are doing any rational thinking about it. And a lot of the times is just because news are not validating their own beliefs so I think it's even worse than just having bad news.
Even without validating beliefs, there are so many cases of news organizations publishing incorrect or misleading information in a rush to cover a story, only to then issue a silent correction weeks later when the damage has been done.
This weakens trust in two ways, first is just people who pay enough attention to notice the correction and gradually lose trust as they see how often that happens. The other is the more damaging, more common way, where someone has read the incorrect/misleading article and internalized the information only to find out much later that the information they internalized was incorrect (without ever seeing the original correction).
One example that comes to mind is regarding the supposed sudden Starlink outages in Ukraine back in October around when Musk was tweeting dumb stuff about appeasing Russia. CNN was quick to report the outage implying that it was unexpected by Ukraine and they were shutdown to blackmail the West into paying. This article was all over the news.
Then weeks later they put out an article stating that it was just 1300 terminals which were being provided by the UK which were shut-off due to the UK deciding not to pay for the subscription anymore, with Ukraine having been fully aware and having swapped them out beforehand with the other ~18000 still operating terminals. But this one got nowhere near the same traction and was still misleadingly headlined.