As humans, we are emotional animals and therefore we always assess the intentions of people in our daily lives. A small collision on road, a person jabbing in the train, a slip of ball out of hand from a player, etc. are all examples where we take a judgment on what was the intention behind the action and forgive the actor. So, it is not that intentions are not important, they are very important and we use them a lot to judge people. Then, why do we hear so much about this intention vs. action argument?
In situations where results matter a lot (either personal or professional), it is very important to measure magnitude or intensity of a result or the action. Otherwise, how else would you make progress. And that is where intention falls flat!
The problem with intention is that the intensity or magnitude of an intention cannot be measured. You will never know how intensely did somebody have that intention. On the other hand, you can always measure the magnitude or intensity of a result. In our professional environments, results matter a lot and therefore actions matter much more than intentions, and hence all the noise about intention vs. action.