Speaking as someone who unfortunately has had to regularly perform CPR on elderly patients... I had a frank conversation with my own grandparents maybe.. 2 years ago (early 80s and up until very recently have been in very good health) and emphasised that the best course of action is a DNAR.
It is a truly horrific act to perform on anyone, let alone someone elderly, and it has a minimal success rate in someone young let alone the older generation.
It is a highly undignified way to die, and I wouldn't wish it on anyone.
At the end of the day... it is down to the medical team, and if they feel it is futile to attempt then they are unlikely to attempt it, DNAR or not, or it may lead to a short attempt and a full discussion of whether continuing is ideal or not.
It is brutal and an awful way to go, with no respect for the patient really. It is nothing like on TV - not a case of a few compressions, shock and hey presto their heart is beating.
In 4 years, I have shocked using a defibrillator once, all others have not been shockable rhythms.
I misread your original post, and if the dr did say that then I understand your frustration, but perhaps he was mistaken or she misheard him.
And as for power of attorney, that only comes into play once she loses capacity to make her own decisions, or if she chooses to give the decision to the powers to decide for her, albeit she has final say.
It is a difficult subject to discuss, think about, and has a ringing sense of finality around it, but there are very few people I would choose to perform CPR on if I could choose for myself. Simply because the outcome is not favourable for the patient, or indeed if their heart does stop beating then there is the possibility of brain damage and a very poor quality of life.