I read through about 3 pages of your debate before I finally decided to chip in. So, in case my post repeats someone else's points, I am sorry.
First of all, if you have a doctorate in something, it is appropriate to assume the title 'Doctor X.' DCs, which I have seen describing themselves in ads, as 'chiropractic physicians' are allowed to call themselves doctors in the sense that they have doctorate, but to me a physician is a MD or DO. ND(nutrition doctorate). I heard of a CRNA (certified nurse anesthetist) who had a PhD who introduced himself as DrX to the pt, while not making the distinction....hmmm..I'll let you form your own opinion on that one..
As for the lawyer who recommends not introducing yourself as a doctor at social events trying to avoid a lawsuit is a little farfetched. You can be sued for anything, doctor or not. It seems a little ridiculous to HIDE the fact that you are a physician or physician resident, for fears of getting sued, while people are sitting down drinking beer and hotwings just because you casually mentioned that you are an MD and told them to ask their doctor about a sleeping medication. You aren't exactly assuming the doctor-patient relationship just because they know you are a doc.
Using the the title inside the hospital as an intern or resident is entirely appropriate, since it does imply MD/DO/DDS/DMD etc and your job is patient care, regardless of licensure status -'all' residents/interns are practicing medicine entirely legal, although terminology on the licenses may cary some variations-it boils down to-you have legal right to practice medicine under the supervision and guidance of your attendings at your institution.
As an intern/resident, you must introduce yourself as doctor, especially if you are assigned to that patient-guess what you are not the RN or the RT or cleaning person- You are doctor X-"What seems to be the problem, Ma'am?"
Your knowlege not sufficient-go find your attending. You are there to become that world-class ER doc, and you have the friggin MD on your wall...that degree is the only reason you are there anyway!
A state medical license is typically applied for after intern year, which is legally a 'full' medical license, which legally allows you to practice 'medicine' in that state. Malpractice insurance that covers you at your residency institution will not usually cover you if you sign up at some small town ER, for moonlighting, etc-you will have to obtain separate coverage.
Last point, the issue of when it is appropriate to use the title outside of the hospital is debateable (sp?). There are some people that do it because their egos are inflated or maybe even deficient, and thus desire respect that they crave. On the other hand, there are those who feel strongly that when they do use the title, eg in a restuarant, that they may get seated faster (I have found a ten dollar bill works better!) or they get treated better. Just be prepared for negative reactions sometimes instead of preferential treatment.