Yes. They're a big organization with a lot of internal controls and transparency and a long history of owning up to mistakes. The idea that they would do something underhanded and manage to keep it secret is an extraordinary claim and requires real evidence, not "it sounds like the kind of thing those jerks would do" from someone who disagrees with their political bent.
A priori, if you expect me to make a factual determination based on what the NYT says, and what Tucker Carlson says, I'm gonna pick NYT unless I see some other evidence.