I guess I can see it from both sides as well, even though the vet is coming across as uncaring, he is still got to make a living after all, but to threaten to put Doyle to sleep is unthinkable, and not a gesture a caring vet would make, so I do indeed have a problem with that, I am sure if he had any compassion at all he would work out something with the owner.
Even thought this might be policy IMO it is wrong of him to threaten to do this, and the bad publicity will do him no favours at all, he should re-think his ideas and come to a compromise, which is after all in the best interest of the pet.,if he really is in the business not just to make money but because he loves animals, he will do this.
Hopefully all the publicity will do some good and maybe funds can be raised to help Doyle's owner pay his bills and have the kitty released to his rightful owner., I can only imagine the stress he feels right now.