It really wasn't. It wasn't difficult for anyone to get past their cheerleading for the Iraq War other than Judith Miller, who (for her service) was given a fake job at a fake conservative paper for a time that I'm sure paid her enough to retire comfortably. The Cheneys and Bushes are media and political darlings. No one paid a price for going with the herd, and doing what the administration demanded.
It was and is difficult for people who failed to cheer on the Iraq War.
The NYT has always been on the administration's side when asked, and "corrects" the record about 5 years after it could make a difference for anyone. Everyone involved gets cush editor-in-chief jobs at "liberal" magazines, or professorships at quarter-million dollar J-schools.
...which says that it's based on reputation. I presume the previous poster's opinion is that the NYT is no longer deserving of that reputation. It's weird that you asked for a citation of their opinion.