I actually don't really know the
particulars of this case, but in general this type of media scandal happens because there are certain people within media organizations who are strangely untouchable - uncriticizable - and while the reasons for that, on the surface, seem to vary, it's always really the same reason: powerful people are protecting someone for some reason, and the normal rules don't apply.
At the NYT this is combined with an extra dose of, "WE'RE THE FUCKING NEW YORK TIMES AND YOU'RE NOT AND WE ARE NEVER WRONG" so things fester.