The thing to keep in mind is that Goodell, in addition to his numerous other unsavory traits, is essentially a reactor. He never leads by example or anticipates issues, he always reacts excessively and in a panic to the latest crisis to hit the league office. He never exhibits leadership or long-term thinking. His main goal is to make the problem go away, as quickly as possible, with minimal damage to the image of the league. So when this issue comes up about Brown, Goodell WANTS to hear that the accusations are minimal in nature, number, and tone. If Mara tells him it's not a big deal, Goodell grasps onto that idea with both hands like a shipwreck survivor onto driftwood because he so desperately wants it to be so. The sooner he can quickly sweep something like that under the rug, the happier he is in his simple, dipshit mind. If he does a favor for the favored owners in the league along the way, so much the better, because that means his bonus will be bigger at the end of the year.
The problem with such an approach, of course, is that once things are shown to the whole world to be far more serious than he initially judged (such as with the Brown and Rice situations), he's been caught with his pants down, and he starts thrashing around wildly to make sure that everyone knows it's not his fault. And then just to make sure of it, he'll revisit and double-down on his original punishments, as if to say he's doing the right thing, instead of people rightly concluding that he's an astounding moralless moron.