My personal interpretation is that Tucker's statement is more or less true and his reading off the names of everyone allegedly involved at the NYT and implicitly threatening to doxx them on the most watched cable news program in the country was an effective deterrent that caused the Tucker address story to get killed. I also believe that the NYT statement lacks candor and that their denying there ever was such a story is a face saving measure.
I freely admit there are other interpretations that fit the publicly available facts and that others may believe otherwise while being intellectually honest.
I actually find observing my own cognitive biases at work more interesting than the underlying story. I know for a fact that my interpretation is driven to some greater or lesser extent by my own confirmation bias. Sadly, being aware of one's own cognitive biases doesn't generally counter the effect. The best I can do is to try to keep an eye on the facts and at least limit myself to beliefs that don't contradict them. For example, why do I believe that the NYT statement is dishonest but the Tucker statement is honest? Firstly of course my cognitive bias runs that way. However I do believe the circumstantial evidence really does support my belief. Tucker was able to name the specific people involved in the alleged cancelled story which implies that either there was a cancelled story or he just made up some names.
Edit: Added some elaboration.