The dog that was killed was in its own yard...her GSD broke away from her and ran into that dog's yard and killed it. How many times on this forum are people saying "stay out of my yard and you won't get hurt." or "My dog can do whatever it wants in my yard." So now you're kind of giving this dog a pass for violating another dog's yard and going in and killing it. Sorry...if you can't have control of your dog on leash, you need to have it muzzled. I had a dog try to attack mine a few weeks ago when the leash "slipped" out of the owner's hand. I didn't care...I have a GSD that protected myself and himself and it didn't escalate...but if I had had a smaller dog we'd probably be discussing a different incident.
I get it...OP wants a normal dog, one that isn't dangerous or isn't thought to be dangerous by the neighbors. And until OP can do that they should do everything possible to make sure something like this never happens again. If a muzzle is an answer in the short term then that's what they should use.
Dogs might not have the same feelings we do about where the grass turns from our grass to the neighbor's grass. So if it was prey drive on our lawn, or on the neighbor's lawn, it really makes little difference in how you react to the behavior, whether you train or manage or socialize or muzzle. It matters, but only on human terms, who is liable for the vet bills, whose dog might be euthanized. I mean, if the dog kills a dog on your land, no one should be able to euthanize the dog for that. But if your dog trots over to the neighbor's and kills their dog, the AC can, generally on a repeated offense recommend and in some cases require euthanasia. This is not to punish the dog, but to prevent it from happening again. And it is the people who suffer, both dog owners will suffer, but one is more to blame.
I don't know about the muzzle. If people could be reliable enough to keep their small dog from plowing into your dog wherever they are, then you can probably do without it. But people are not reliable. People let dogs get right up in other dogs' faces all the time. People use flexi-leads and their dogs just go wherever. People leave their dogs loose, and they charge up.
Frankly, while I will blame the small dog owner for letting their dog be eaten in the above -- off the property incidents, like on walks, at the park, etc.; I do not want my dogs to attack another dog, not ever. This means I have to be proactive to keep that from happening. I do this by taking my dogs to classes during their first year until I feel they are reasonably reliable around other dogs in all situations. And so far (searching for wood to bang on), they have not cause injury to another person's dog. If I had a dog that I knew would, I would probably use the muzzle and prong collar. It is all about protecting my dog. If protecting my dog means protecting your dog from my dog, so be it.