After what was probably the most impactful case of news media influencing public opinion in recent memory–the NY Times / Judith Miller reporting on Iraqi weapons in 2001-2003—the NYT did in fact publish self-critical pieces.

https://www.nytimes.com/2004/05/26/world/from-the-editors-th...

https://www.nytimes.com/2004/05/30/weekinreview/the-public-e...

https://www.nytimes.com/2005/10/16/us/the-miller-case-a-note...