To further clarify, if the newspapers has anything to do with the act of giving them classified documents, they are guilty of a crime. So if you walk into the NYT and say " I have these secret documents, want them" they are fine and can publish them and (depending on how you got them) you get to spend a long time in jail. If a reporter comes to you and says "hey, can you sneak out classified documents" and you do, you both go to jail.

It's worth noting that news agencies will often give the government a chance to explain why they should not publish the files in truly important cases. If that's likely to be "if you publish the plans for D-Day, many people will die. So please don't"