Re helicopters and dogs, excellent points.
Helicopters are in short supply these days for the obvious reason even if they could assist rescues in difficult terrain of the Whites. For a serious injury, plan on being carried out, which takes awhile. F&G does not have enough personnel to assemble the 30 or more people it takes to carry out from higher elevations. They rely on the various volunteer groups, AMC, etc., whoever happens to be closest. It can take awhile to call out all those people, get them to the right trailhead, get organized, hike up and find you. They're dragging a litter and maybe an O2 bottle and other supplies and each SAR volunteer is carrying a pack heavy enough to support himself or herself for 24 hours during the operation, too. (Although in this case the litter was probably at Lakes hut.) In really difficult terrain at night if your injuries are not life-threatening but disabling, someone might take care of you overnight on site until first light makes it possible to carry out safely.
Re dogs, I remember an incident on the Nancy Pond Trail. A woman with four (4) dogs broke an ankle. There were two large protective type dogs (shepherds, I recall) who would not leave her and two smaller dogs who would. Four or five of us hikers found her. I walked out the two smaller dogs, one person stayed with her and the two big dogs, and one or two other trail runners sped down to the trailhead to call for help. I realized when I got down that I didn't have phone numbers for contacts to call and come get the dogs in case it took awhile (overnight) to get her out. It would have been a good idea if I knew something about the dogs I escorted out. As suggested, an "emergency plans and contacts" sheet on the dogs would have helped tremendously because the focus, of course, will be on details about the human victim, not the canine companions.