If a property owner has a dog that they use as a free range tool that's great as long as it is restricted to their property.
If I want to go target shooting in my own back yard and my state or provincial laws allow for it that's fine too, but as soon as that bullet leaves my property line I am responsible for it... same as the dog.
There is no comparison between a dog and a deer, unless the deer is owned and domesticated.
The fact that the owner inquired if they were going to have their dog replaced just exemplifies that some folks have little to no common sense.... and some are just plain stupid.
Forget the fact that it is costing you money, time, effort, or that it could have cost you your life, consider that when you go after them civilly or via their insurance, they may think twice next time about allowing an animal to do whatever it likes.
You may be saving another rider, or more importantly, a child's life one day.
There are always two sides to every story, but if we take it for as it's posted, this was not an "act of God", it was caused by was the inaction of an irresponsible member of society.
Some people shouldn't be pet owners or parents either for that matter.