From 2000 to 2007, I ran a small feral cat rescue group on Saltspring Island. I did not have the funds to have the feral cats tested for FIV or FeLeuk, but they were all given a vet check, vaccines, deworming, etc. at the time of their spay or neuter.
The first feral cat I rescued was while I was still working for the SPCA. I was called to book him in to the SPCA on Saltspring. Instead, I took him home, and still have him - over 8 years later. He developed URI and both of the vets who treated him (the vet office rented space to the SPCA, and treated the SPCA cats) told me that cats like him would be better off dead, and that in their opinion, the SPCA would not pay for his treatment. That was never verified, of course, as I was so upset at the vet's response, that I said that I was taking over full responsibility for this kitten and would pay anything necessary to ensure his recovery, and instead of taking him to the SPCA, I took him home. In fact, a 10 day treatment with antibiotics, and loving care turned a sick kitten into a healthy one. I have treated other cats who have had URI successfully and would never consider it a reason to have an animal killed.
The only times I have had a vet euthanize any animal has been those times when my own cats and dogs have reached old age with an illness that is both incurable and is causing them suffering. That to me is true euthanasia - an end to incurable suffering.