Why did Brinker assert that it was necessary to address the reality of Finny's physical disability??

This is actually a pretty involved question. To state it plainly, Brinker has no stake in the matter, and no motive in his actions that is discernible from the text. He has no way of knowing what went on, and no sources to draw on in order to create his "theories." The patchy motivations and the indistinct characterization of Brinker make him seem like another symbolic figure. It is as if he were a creation of both Gene and Finny's inner conscience, reluctantly spawned by both of them as a way of forcing themselves to confront the realities of the accident, and their state afterward. Brinker operates on a more allegorical and less realistic plane than a character like Gene.

The inquiry itself is rather odd, since neither Gene nor Finny consent to it or want to take place in the proceedings. Brinker resides as the chief of the proceedings, hell-bent on getting the "facts" into the open for everyone's own good; how ironic, since it is the disclosure of the facts which causes Finny's second accident, and puts a great traumatic strain on him and Gene. As Gene says in his apt metaphor, Brinker is "imagining himself Justice incarnate"; but even Gene knows that Brinker is going at this from the wrong angle, since "Justice incarnate isŠalso blindfolded," while Brinker is trying to get his desired outcome out of the whole affair (161).