You absolutely can publish stuff which is known to be false in the Daily Mail, which is one reason it's a tendentious rag. I don't know enough about the NYP's attitudes to known falsehoods to know if that's true for them or not. I would be astonished if a politically useful and commercially popular story were spiked by Breitbart because the editors weren't sure it stood up. This is common even with papers like the Guardian, who are way less fastidious than the NYT and WP.
But sure, story selection is for sure a product of what a given outlet considers 'newsworthy', which has political bias (conscious or otherwise) baked in.
But sure, story selection is for sure a product of what a given outlet considers 'newsworthy', which has political bias (conscious or otherwise) baked in.