He sounds very argumentative, except at one moment where he agrees that he 'understands that' it is important to protect the confidentiality of Lynch's team.
Her argument is that it's very important that these decisions not be touched by politics. That is to say, in this case, that it is important that they not have to explain themselves to the American people. This is being presented as an interest in justice: that it is important to justice itself that these decisions not only be made out of the public square, but that the explanation for the decisions never be revealed to the public at all.
And that's the part that Gowdy buys.