Really? You're not concerned that government employees may be picking up some income on the side by leaking stories to whichever news outlet pays them the most? That's just a weird thing to be worried about?
I agree that we want accurate information about government abuses to be smuggled out. But that has nothing to do with this situation.
This situation is about one newspaper getting a commercial advantage from publishing information a few hours earlier than their competitors. It reduces the quality of information the public sees, because many people will read only the report they initially see in the NYT, which includes only the commentary by people they decided to talk to. Whereas if all the papers got the information at the same time, people seeing the initial reports could flip between several sources of commentary, and possibly get a more balanced set of views.
As far as I know, there is not a finite allowance of time the public is provided to digest information before forming opinions on it.
That one outlet may have a slight time advantage over another is always going to the case (efficiency and process variations). That one outlet may have a slight informational advantage is always going to be the case (better sources, better journalists).