[delacoert]

It means to publish someone else’s work.

That makes sense, thank you.

Could they dodge editorial responsibility this way?

One could imagine a clever way of taking credit if whatever the story is pans out, or playing the victim if it's bogus. I guess it all depends on the way they present the exposé (if they publish it all).

[CARTOUCHE]

Could they dodge editorial responsibility this way?

I doubt it. In Drudge’s parlance it may also means simply that the Times is going to put it on the Front Page and whether it is above or below the fold gives the story more importance by NYT standards.