The title of Doctor is a professional title earned by someone. If you called someone Mr. Johnson knowing full well that he's a doctor. By not calling him Dr. Johnson (even if he's not your personal doctor) is unprofessional. Especially in this case where he is a paying customer and his reason for not wanting to miss the flight is because he has to go see patients.
I don't see people calling him Dr. Dao. I see people saying "he's a medical doctor, he should be treated better." As my post after the one you quoted said, I think that draws favoritism towards a certain occupation and I don't particularly think the favoritism is warranted.
Just as his past criminal record or what not has nothing to do with the shitty treatment he received, I don't think we should favoritize his position because of his role in society.
My problems with the case are:
1) Airlines can kick people off because they can't get their logistics correct
2) Airlines can kick people off after they let them on the plane
3) Airport security can hurt a person in the process of kicking them off a boarded plane
4) Airport security can then issue a report lying that the man fell
5) Airlines can then issue a statement not acknowledging the assault and then paint the man as belligerent
6) Media want to victim-smear afterwards
I think those should be independent whether he is old, young, doctor, thug, whatever. I feel worse personally because he is an older gentlemen and I believe older people need more protection in society, but that's independent of the problems of the case.