People in positions of authority have to be really careful. I would certainly be fired if I used my position to witness - politics, religion, or personal opinion.
It is the same thing in other postions, e.g. teaching, law, etc. Praying and asking for wisdom to speak or not to speak and the right timing is important. I don't know the details and whether or not the patient seemed open to this. Or just what and how this was said.
I do recall over 20 years ago when I was given a forecast at what might be the result of six months of chemotherapy treatment, i.e., how long I may live. The chemo doctor said.."You could live 2 years, 5 years, and maybe 10." So, I said.."In other words this is in the hands of God." And he said, "Yes." I went with that as encouragment and honesty. Of course, I am the one who introduced "God" into the equation. btw, I have lived 22 years since then. And, thanks be to God, no more chemo since. God was in the healing process and still is.
It sounds though like the mother is over reacting to something which could have been basically good for her son. We need to pray for this doctor who likely acted out of courage and conviction that this would help the patient.
I feel compassion for this doctor. But I really don't know what he said and how he said it and I don't know what type of person the doctor was. Just because he was a Christian does not necessarily indicate to me that his comments were appropriate or wise. Still..good to pray..