Our cat had fight wounds and an abcess on his hip. The first vet saved him but sent him him home with a tightly wrapped IV stint still in place. Late that night his paw was swollen and his claws were turning blue. We called the Emergency folks and they advised to cut the wrap, pull the stint, and massage his paw. Of course there was no fee. I thought they cared.
This morning Tony is walking on all four paws: full weight on each, no limping, and is his usual self again. Sounds to me like your dog was too shot up to make it and the hospital did a triage-type decison. I'm sorry your dog died but you should not blame the hospital.