It is? Really?
I've had a couple of kids in daycare and I can remember nothing close to ' All of your childs possessions are our responsibility, if anything becomes lost or damaged, we will gladly be held responsible...."
Exactly. Yes, I'd be annoyed that my DD's coat was torn, but it's daycare and I would just fix it myself and move on. I would not expect you to pay for it or fix it.
My rule is: don't send DD to daycare with anything we don't want ruined. These kids spend all day painting, eating, playing on the playground, etc. Clothes are bound to come home with stains and rips. I don't blame the teachers, I don't blame my 22 month old, I don't blame the other kids and I don't blame myself. It's the nature of the beast.
Even though our DD's clothes are clearly marked, she came home with someone else's pink coat a couple of times in the beginning of the Fall. The teachers were just learning which coat belonged to which child and there were a few mix-ups. No big deal.