It is hard to compare the S&R teams to a family on a hike. S&R is full of experienced healthy adults. No infants traveling on a front pack.
And they have plenty of water and emergency supplies and are in contact with helicopters in case of the earliest signs of trouble.
I think the infant and doggie were in the earliest signs of distress and that triggered an unfortunate series of tragic events. A S&R team would have the ability to respond to that kind of emergency without endangering the rest of the crew.
I have experienced my 18 month old son, being carried in a backpack by my husband, beginning to exhibit signs of heat exhaustion. Thank Goodness we were not in a remote area on a hiking trail. We were at the LA Zoo in August and were able to get him to a medical tent within 10 minutes and they jumped into action.
I had no idea how serious the situation really was. But they immersed him in water briefly, then laid him on a little bed with ice packs on the back of his neck and on his chest. We were in the a/c and they turned it up to help him cool down faster.
When we arrived at the tent he was sluggish, pasty white, skin was beaded with sweat, and he looked exhausted and was almost unresponsive. It was frightening.
Within minutes he was crying and fidgeting and having a little tantrum and the doctor was very pleased with that reaction. He said it would have been much worse if he continued to be passive and weak. So getting annoyed by the fuss and chaos was a good reaction on his part.
But if their baby girl had the same symptoms, I can't imagine how they could have reversed the symptoms, while out in the blazing heat. We had ice packs, cold water bath and a/c and shade. They were considering giving him an IV of fluids but decided he didnt need it.
All the Gerrish family could do was pour some of the precious water they had on her and try and get her to drink as much as she could. But that is not enough to reverse Heat Exhaustion and she likely progressed into heat stroke at some point.