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.
Unfortunately, having "DNR" tattooed on the chest probably wouldn't be sufficient. When I did EMT training, we were taught that unless we had an actual hard copy DNR in our hands, we should always attempt to resuscitate. Even if there was a family member there telling us there was a DNR, we should still resuscitate unless they handed us a hard copy DNR. The reason is that sometimes one son or daughter thinks it's time for dad/mom to go. But another son/daughter who is not present will think otherwise. If the EMT does not attempt to resuscitate (even if told not to by a family member) and it turns out later that there is not a formal legal DNR, that EMT could be sued by another family member.