Kohli lbw b Hazlewood - did DRS get it wrong?

Australia vs India, Day 3 of Test Match #2.

The match is at a critical situation. The series is in balance.

Hazlewood to Kohli. The ball is on target but keeps low and Hazlewood appeals for lbw. The on-field umpire rules Kohli out - he must have thought either Kohli didn't hit the ball or that he hit it after the ball had struck the pad.

Kohli thinks it was the bat that hit the ball first and asks for a review.

The Third umpire confirms bat hit the ball, but is not sure whether it hit the ball first. So, as the DRS rules prescribe, he says the replays are "inconclusive". He leaves the decision to the on-field umpire.

DRS rules 3.3 (k) and (l) say what must be done next: "The on-field umpire must then make his decision based on those factual questions that were answered by the third umpire, any other factual information offered by the third umpire and his recollection and opinion of the original incident. The on-field umpire will reverse his decision if the nature of the supplementary information received from the third umpire leads him to conclude that his original decision was incorrect."

Returning to the match situation, the on-field umpire now knows that even the third umpire, who has access to UltraEdge and slow-motion replays from many angles, is unable to conclude whether the batsman is out or not. How then could he be sure about his original decision? When the umpire is in doubt, he cannot rule a batsman out. But he sticks to his original decision and sends Kohli on his way. Rarely does an umpire reverse his decision. What does this tell us?