It is indeed very sad that the dog died. 
However it’s not a case of the owners bearing some responsibility. They bear ALL responsibility. According to the article, the dog has been in the neighbor’s yard numerous times. That’s not a “loose dogs happen by accident” issue as much as a “whatever” attitude by the dog’s owners.
The dog suffered due to human error. But the error lies solely with the dog’s actual owners. But everyone will feel bad for them and villify the man using a legal means with a legal firearm to protect his own animals.
Also in many areas in NH, it’s legal to fire your weapons on your own property. Doesn’t make someone trigger happy. It’s just someone who enjoys a legal hobby that others find scary or creepy.
Not to mention New Hampshire is a very serious state for protecting firearm rights and property owner rights.
I do feel 100% bad for the poor dog though. Got stuck with naive homeowners who failed the poor pup and now want to blame others for their own lack of training and care.
I do also feel for the dog owners, it’s sad to lose your dog. I hope they learn to do better by the next dog if they get another one and that they own up to their own blame in this.
Although I’m sure the media will play up the “murdering mad man with an assault rifle” angle…heaven knows the uninformed, biased and incapable of research media LOVES to villify firearm owners/users and “country folk” as backwoods freaks.