First responders always respond to medical emergencies - that's the point. The independent living facility apparently - despite their subsequent denials - didn't want to be put in the position of a first responder to cardiac arrest. I would be confident that the same facility would respond to a fall, or a fall resulting in a severe cut, differently than the decision to perform CPR. This woman had her heart attack in the dining area, and a similar fall resulting in pain to her hip or bleeding to her head would get approximately the same medical treatment - call 911, otherwise keep the patient immobile until arrival. Apply pressure to the cut to reduce bleeding, but otherwise do not administer first aid. You have EMTs 7 minutes away. You would be nuts to move a woman with a broken or dislocated hip, or to begin to apply dressings to a head lac, which just have to be ripped off when the EMTs arrive on scene.
It sounds very much like the woman's family was aware of her wishes to die naturally; however, a 911 operator can't assume that, or accept it from a facility director, or even from a member of family. It seems as though some who are responsible for the care of the elderly are arguing for any 911 operator to make a call about resuscitation of the elderly - again, she fell in the dining area, away from her room or apartment. What if she had a DNR, could the facility produce it in time to ward off the EMTs, or the appeals of the 911 operator for kitchen staff to begin CPR? In my MIL's facility DNRs are posted just inside the front door of their residence, shared with management, and I believe they are also proactively shared with the local FD who respond to the facility (they keep them in a binder). But they aren't shared with 911 operators obviously. I think its up to families and people themselves to sort out whether to DNR or not to DNR - a decision once made that makes the care considerations crystal clear, provided everyone nearby knows about the written DNR and can produce it quickly enough. If you find yourself living in a facility, they should be able to advise you on this too.
Before dementia really took hold, my Dad joked about having DNR tattooed across his chest so that anyone ripping open his shirt to start compressions would be faced with that, luckily for us that never came up. Dad died naturally too, and despite very labored breathing near the end, he was never intubated or had any meds to prolong his life beyond what could be expected to make him comfortable. And even that was a very hard decision that split my family in the last 24 hours of his life - whether to transport him to an ER and prolong his life (or suffering). We all respond differently to this for very natural reasons. And the more I mention this, I recognize that almost everyone has a similar story along the same lines that informs their views on dealing with death. There's probably no one response to it all.