It goes back to what Captain Pike said to Kirk when he first met him. He said that Kirk had a tendency to jump first and ask questions later and he felt Starfleet had lost that ability and was becoming so cautious and risk averse and that it was not healthy. (Or at least he implied most of that with only a sentence or two.)
Kirk was the one who had gone with his gut, after putting all the facts together, and had come up with a conclusion even Spock (who was against Kirk at that point) agreed was good logic. And when Kirk had come to that conclusion, he was willing to jump in and take whatever risks he had to so he could bring the point to Pike's attention.
That he was on the Enterprise when he shouldn't have been and even made it on to the bridge when he should have been caught and put in the brig -- and then, on top of that, had come up with a correct evaluation of the situation when nobody else had put the facts together, proved Pike's point: Kirk followed his gut (which was always a big part of his character), jumped first, then worried about the questions. That validated not only Pike's view of Kirk, but since no one else had put the data together to get the same conclusion, also validated his view of what was missing from Starfleet.