We can argue until the cows come home whether or not Pit Bulls and similar breeds are "mean", "aggressive", "dangerous", etc. It DOES NOT MATTER how nice/friendly/etc. "your" dog is. The breed(s) in general have aggressive characteristics in them and have killed/maimed people.
We can also argue about how personal raising/training has EVERYTHING to do with it. However, a toy-poodle, no matter how it is raised/trained, is not going to rip a grown man to shreds.
I love dogs and like the breeds in question, however I would not have one in my house with children around. (This is not to inflame, I just don't trust them.) I have seen dogs ignore their owners when the right conditions are met... and the owners have trained their dogs properly.
I also do not believe in having to act/behave "correctly" around my dogs. I train them to not be agressive no matter what the kids are doing to them. Nothing pisses me off more than to have a dog growl and/or bite a kid... only to hear the owner say "your kid should not have done that". Priorities are really messed up here. I'm not talking about a kid being aggressive either.
Anyway... sorry for the rant, that was not the real purpose of my post....
All of this "treat the neighbor's dog nice / get to know the neighbor's dog / give the neighbor's dog treats" are touchy/feely to some, however a land owner should not HAVE to do that. I agree it may work for some, however if a neighbor does not have control of their animal, it is not the land owner's job to deal with it. Plus, if a neighbor loses control so the dog goes on a land owner's property, chances are that neighbor does not have control to prevent an attack.
Don't lose control of your dog and you wont have to get upset about said dog being put down. Don't blame it on the land owner.
Btw, I like dogs (I mentioned that ealier I think) and like to get along with all of my neighbors, however all of this IS NOT the land owner's problem. Just quit with all of the excuses and quit with all of the things the land owner should try first.
If I feel threatened by an animal (chances are my wife and/or kids will feel threatened as well) while I am on my own property, that animal's days are numbered.