That being said, Woodward and Bernstein didn't publish verbatim what Mark Felt (aka Deep Throat) told them; they used his tips as starting points to look for corroborating evidence, which they published to great accolade.
The WaPo and other mainstream media were also institutions of far more integrity at that time: their mission was to publish truth regardless of the implications, and they weren't under the kind of pressure the press is under today. Also, society (and media outlet owners) trusted truth itself to result in societal good far more than they do today.