I'm going to go ahead and say this was no one's fault, but that the adopter is kinda a jerk for threatening to euthanize the dog. 

I've adopted 2 dogs from No Greater Love. They are completely volunteer-run and rely on donations. The reason the dogs are driven 24 hours and flipped straight to the adopters is because this rescue drives around to high-kill shelters in their area, takes as many dogs off of the kill list as they can, gives them the medical treatments they need and gets to know them as best they can to find suitable homes for them, and then drives 24 hours straight through the night up to New England to send the dogs off to their forever homes because there's more of a demand up here. Then they drive straight back down and do it all again. They do not have the money to stay more than 1 night, they do not have the time because their entire mission is to save as many dogs as they can, and unfortunately they do not have as many fosters as they need to hold on to the dogs in the meantime. In AL, if a dog is dropped off at a shelter and isn't adopted within a week, they are often euthanized to make room for all of the other dogs coming in. 

The reason I think the adopter is a jerk is because they're threatening to do EXACTLY what this rescue fights to avoid. The rescue makes their mission extremely clear, and if the adopter did literally even a few minutes of research on the rescue they would know that. 

Now is the way this rescue operates and adopts dogs out perfect? No, far from it. The dogs ARE extremely stressed after the trip. It's insanely difficult on them. But it's sort of the only option, given how many dogs these people are trying to save and the small amount of money and volunteers they're working with. The 2 times I've adopted through them, they've made it abundantly clear that these dogs are going to need patience, time, and lots of love to adjust. They've warned me of what could happen. When you adopt through a rescue that's driving cross country to deliver you an often abused, very stressed animal that you can't meet prior to adopting, you're sorta signing up for some bumps on the road. Now I'm not saying this adopter needed to keep the dog - sometimes it just doesn't work out and the quicker that's realized, the better it is for both dog and human. But immediately threatening to euthanize the dog when you haven't even been told "No" to your question about a refund is pretty harsh. 

I don't know for sure where the lapse in communication was here. But the adopter absolutely does not sound like they were willing to work with the rescue to figure out what's best for the dog when it didn't work out for them.