It isn't clear from the rather superficial article, but the chances are the helicopter was involved right from the get go. It is more and more common to use a helo in the initial stages of a search operation.

Once the chopper is on scene, you might as well use it for evacuation. I doubt that any ground team, faced with a dog needing evacuation, would call for helicopter assistance.

Pet rescue is definitely a gray area, but our unit almost always responded - for the training, if nothing else. For years ad years the largest voluntary contribution we ever received for any rescue operation was one where we lifted a stranded doggie from the depths of a mine shaft, which is not a trivial undertaking.