I just can't seem to help myself. I really just wanted to drop this one, but I couldn't. I apologize to all the people who are aggravated by this, or don't give a ----. Yes, this is a few steps too far.
I found the statute for the state of NJ. It's a state board of medical examiner's statute, to begin with, and simply states that if you claim to be a physician and to practice medicine, you must actually be one.
Emphasis mine, weird punctuation theirs.
Any person shall be regarded as practicing medicine and surgery, within the meaning of this chapter, who shall use the words or letters '"Dr.", "doctor", ""professor", ""M.D.", or ""M.B." in connection with his name, or any other title intending to imply or designate him as a practitioner of medicine or surgery in any of its branches, and who, in connection with such title or titles, or without the use of such titles, or any of them, holds himself out as being able to diagnose, treat, operate or prescribe for any human diseases, pain, injury, deformity or physical conduction, or who shall either offer or undertake by any means or methods to diagnose, treat, operate or prescribe..."
Paraphrased: Anyone who calls themselves something that sounds like a physician AND (this is important) either tries to treat or says they are able to treat an illness as a physician, must actually be a physician. The intent of this statute is crystal clear if you read the whole thing: to prevent faith healers and other "practitioners" from calling themselves physicians if they are not.
If your reading were right, it would be "illegal" or whatever you want to call it, to call yourself a professor unless you were a medical doctor, too.
My opinion on the whole matter, and my final word, and then I'm getting back to my life, and not this trivial sh--:
Introduce yourself as whatever you want. It would be confusing to call yourself Doctor if you are not a medical doctor or dentist, so probably a bad idea. You can go by Mr or Ms, but I know of few people who are comfortable with that after they have their doctorates. How many MDs would go by Mr or Ms at a University? You've got to figure out what you are comfortable with. In the end, it's your call. Anyone who says anything different is either a lawyer, or shouldn't matter to you.
Now, can't we all just get along?