I will admit to not reading this whole thread. It made me too angry to read over and over again, how "simple" euthanasia is. Just disgusting. I'm sorry, but if this was an indoor dog who lived with her owners for 10 years, I doubt that they find anything simple at all in this situation.
Not one of the offered choices, but I'd keep my dog. I'd tell the insurance company she was gone if I had to, but I'd try to get other insurance first. But I would keep my dog.
For all of you "oooh, if my dog bites, it's getting put down people" do you believe MY dog should have been put down?
My oldest greyhound ( going on 12 ) was adopted from a bottom feeder track at almost 5 years old. She had lead what I can imagine and awful life prior to coming here. Fear made her catatonic. She'd pace for hours, would not enter a room that had humans in it. She'd hide in my dining room and cry and cry and cry. Every part of her becoming a pet had to be learned. For her to be completely normal to immediate family took almost two years. She still won't walk up to any standing person from head on. If she wants to see me and I'm standing, she'll sneak up behind me for petting.
Anyway, my stepson at around 16, came to stay with us. He didn't like me much and he did not like Hannah. She'd bark and growl whenever he entered a room. It wasn't aggression, it was fear of a new human male, something she'd had many bad experiences with in the past. Well, one day while my husband and I were grocery shopping, the stepson put on a "Jason" Halloween mask and chased her around the house. God only knows why..

MY daughter called me on the cell and told me what was happening and I came straight home. Well, a couple days after the incident Hannah bit my stepson. He walked right up to her while she was barking ( which got ten times worse after he chased her ) and she bit his side. I yelled at her and took her away from him. He got reminded again ( you'd think he'd already know that at 16 ) that scaring animals half to death is not even remotely funny. Quite frankly, that bite was his fault.
So, now, probably 4 years later, Hannah is sleeping on her dog bed. Stepson has joined the military, married and gone. He visited for Christmas. Hannah still doesn't trust him, she barked like crazy and then let him pet her a little then ran away. She's fine ( basically stays away from ) any other stranger and hides in the dining room.
Over my dead body would they have put my dog to sleep.