I think this whole issue is just one more rural vs urban thang, and that the "right" answers to the questions posed by the first post depend almost entirely upon where you live.
City and suburban folks usually can only conceive of a dog as a pet -- a pet that may be mistrained or mishandled by the neighbors, but which is of course the responsibility of someone else, and is usually under the direct control of some human. They have a hard time wrapping their brains around the concept of a dog that literally belongs to no one, a dog for which no human being has any responsibility or care whatsoever.
Rural folks, when they see dogs on their property that are not their own, know in their bones that this animal is wild, belongs to no one, can carry nasty diseases, and, left alone, will do damage to their property and belongings. They have a hard time wrapping their brains around the concept of a dog running free that belongs to someone, that someone might care about.
City and suburban folks, seeing a stray dog, immediately think to call Animal Control so that someone else will quietly "put the animal to sleep" somewhere else.
Rural folks don't always have access to Animal Control, and are used to solving such problems for themselves. So they'll "put the animal to sleep" in a more noisy, direct, and messy fashion.
In either case, the usual outcome for the animal is a quick, clean death. Which is as it should be, if the animal has no one to take care of it properly and is either a nuisance or a hazard to human beings.
As for the post which started this thread: Shooting a dangerous nuisance which belongs to no one may be sad, but it isn't wrong. Setting out a pan full of poison in hopes the problem animal will drink it, though, is something else entirely. Not only can poison cause a painful, slow death rather than a quick easy one, but you have no control over which animal drinks the poison.
If you live somewhere where simply shooting a problem animal isn't advisable, then you live somewhere where a quick call to Animal Control should take care of the problem.
pax
Why is it that city folks never believe outdoor folks, when it comes to animal behavior? -- Art Eatman