How sad for this poor kitten. I started volunteering at our local shelter two weeks ago. I'm certainly no expert and have very few days of experience, but I do know that all of the kittens/cats have their ears cleaned and checked before going out the door to petsmart. They are also wormed, and vaccinated. They come with two months worth of health insurance that has a $50 deductable and can be used at your own vet. Most of the petfinder websites I have seen offer this with their adoptions. In my few days of experience I also find it hard to believe that they did not know he was vomiting. I guess its possible that he was in a cage with several others and it somehow went unnoticed.
I would also be concerned as to whether this vet should be postponing surgery. Can you go and visit Dusty? Since you have gotten to know him you should be able to tell how he is feeling. Maybe you could make a decision after spending some time with him. Maybe you could make an appointment and meet the shelter vet and see if you are comfortable with his findings and see if you feel that he has the kittens best interest at heart.
It's such a shame that you did such a wonderful thing by adopting a shelter kitten and then had a bad experience. I hope that Dusty is ok and you can get the situation resolved soon. Please keep us posted.!!
There are a lot of people on here that deal with shelters and have for many years. I hope they can be of more help to you.