Asking for a doctor in an ER - here comes the physicist!
If you stagger into an ER and ask for a doctor, do you *really* think a non-medical doctor is going to say, 'what can I do for you?'
The criticism against non-medical doctors using the title is blatant, ignorant prejudice from people who don't understand what 'doctor' really means - someone who holds a doctorate*. And when they first learned that it doesn't just mean MDs, but also PhDs, they were probably embarrassed and had to take a contrary view and are too proud to acknowledge otherwise.
That said, I hold neither a doctorate nor a master's, bachelor's, or even associate's degree. Just a simple high school diploma with a few credits at university and quite a few years working at one with plenty of doctors, medical and not, whom I highly respect for their dedication and knowledge.
*Or, apparently in the UK, a medical bachelor! Which is news to me; and I've lived in London with a partner who's a nurse practitioner for about eight years!