From my POV, the key things are trust, empathy and good communications both ways for good sits, especially when something bad happens.
Sounds like the sitters and hosts have some of those elements in this case, though the question about how to CYA seems a little odd to me. But maybe the sitters sense something off.
For me, I never had doubts about doing what I think the hosts would want. And they ended up writing me a review that said I did everything they would have in an emergency and I showed great care. (I think the most important thing is actually to pick hosts at the outset whom you think would be strong partners if anything goes wrong, especially with a sick dog. And would show trust, sound judgment and grace even under pressure. Likewise when choosing sitters. Otherwise, to me the sit isn’t worth doing at all.)
In my case, my sit dog was elderly and had been diagnosed three years earlier with heart problems and other issues, was on five medication applications daily. And I’d flagged an increase in coughing early and the hosts trusted me to adjust that med if needed, within parameters they’d previously discussed with her regular vet.
Yet she still had daily quality of life. She played, ate well, stalked the neighborhood cat (her nemesis) and barked at other pets and people like normal, enjoying every walk.
Then 11 days into our sit, she had back to back catastrophic seizures while we were in bed together. I rushed her to urgent care that night. They stabilized her and monitored her, then suggested that she be put down for her own good. I offered to stay with her through that, so she wouldn’t be with strangers at urgent care. But her humans scrambled and cut short their trip, which was on the other side of the world. I considered that fortunate for their dog and would do likewise if it were my dog.
We stayed in close comms and coordinated so that we’d meet up at the urgent care late at night after their return, so we could all say goodbye to their dog. They even brought a few friends and family, who’d also loved their dog.
They were strong communicators, so I knew their flights, including their rush home. And they offered to pay for a hotel for the remaining original six sit dates. I ended up paying for myself instead, because I knew they’d laid out a lot and were expecting a baby as well. (I never take sits where I can’t cover myself with a Plan B if something goes wrong.)
After she died, they created an online memory book. I added my recollections and photos of her last days. She was much loved by many and had great adventures, lucky dog. She was a sweet soul and I keep a photo of her on my desk.
It’s never an easy choice.