I have had my first real issue with Sainsbury's today, but their customer services was good - despite paying for tigers last claim including euthanasia, they forgot to cancel teh policy and sent me renewal forms today!! Think she said they are going to refund the premium I must have paid last month (should check bank statements better!!). But, the bonus is that even though they paid out hundreds of pounds, it was still less than £14 a month.
US - every insurance company will pay for the treatment upfront, however, it is up to the vet whether they will accept it, so you need to ask them rather than being in a position where you might struggle. From the posts on here, it seems like very few vets do accept it (although the specialist we went to did), and I Can't blame them - Pebble's first claim took 6 weeks to come through.