The thing I wonder about homeowners insurance is do they factor in the statistic on how homes with dogs are less likely to get burglarized?

Good point, but I think they are more concerned about the biting issue and mauling.
Which brings another good issue to mind-what about the laws designed to protect people against dog bites - In our area, if someone trespasses in your property and your dog bites them-the dog can be considered an endangerment.
It depends on who trespassed, and what signs you have posted, and the dogs history of course.
But it is still unfair, because every dog is different when they are in their own home and you are not there.
I have a friend who's shepherd bit a teenager because he jumped the fence to retrieve a ball. He didn't really "bite" him because he didn't do any major damage-some scratches from his teeth and maybe a bruise-but he knocked him down. (let's face it -if he wanted to hurt him0he would have done major damage)
But the dog was confiscated and there was sorta a trial-the dog was given a "mark" against him and the people were warned that if he recieved another-he could be PTS.
They had "beware of dog" signs up, but because it was a "child" they said they couldn't be sure he could read the signs.
What a load!!