The fact is that firefighters have been helping families with their wayward pets for a very long time. I think it is a good tradition and not a waste of money. It would be far worse to make taxpayers suffer because no one would help them.
In this case, the firefighters should have just told the family over the telephone how to free their pet
A couple years ago, a skunk got his head in a mayonaisse jar. A cop shot the jar with a pellet gun, breaking the jar and freeing the skunk.
Quick and painless.