I have to say that I really don't think your vet should have put you in that situation. I don't understand why he would have to go to a new home for them to do the surgery for free. It doesn't sound like the person who would be getting him would be footing the bill, or really doing any of the surgery. I would call the vet himself and explain that you really appreciate what they're doing, but that you don't see why they couldn't do it free or for a reduced price for you. I just think he's put you in a worse situation emotionally than you would have been in putting him down.
I guess I have that question too. Would that person pay for the surgery, or would it be done for free and they get to keep the dog?

See, that's not right.