Unfortunately, no one's about to attempt to even slap the NYT's wrist, much less prosecute them. The NYT probably has dirt on just about every congress critter to insure their silence.
If the NYT had dirt on Republicans, you can bet they have already used it. But your point is probably true just the same. Newspapers have a valuable cash equivalent thing to bribe with: focus and opinion. They don't have to have real dirt to imply and distort. Doubt and suspicion can kill a reputation, especially if it is repeated often enough.