That's an interesting observation... it's true I don't check the news I find plausible as much as the news I am already sceptical about, while I mostly become sceptical about the news items not because of the reporting/writing itself, but because of the alleged facts not matching my expectations / biases.
It's a messy problem, as checking news items takes a lot of effort and it's just impossible to deal with the news volume nowadays. Ideally I'd love to see some cooperative effort to check news items by many people with different ideologies/biases, but I think there's currently not enough manpower for that and it's also very easy to end with a biased set of checkers.