I think you are wrong on this one.

1. it is very easy to find you as the one below mentioned, IP address and the timing you used the computer.
2. If you stop your car to offer and things go wrong, you are in BIG trouble. If you are not offering any helps even people know you are a physician and pissed, you are still fine. by internet, taking money is for sure to put yourself on the chopping-board; not taking money but offer medical advices, I am not sure and that was the reason I was askintg.One thing I knon for sure is if you offer (by phone) free advice for people you know, as a practiciner, you put yourself in the same situation as you regular practice.

My guess is:

By internet, as long as you don't claim you are a Physician, especially not saying you are a US board certified/licensed physician, you should be fine, as the reasons you already mentioned. But I don't know the answer for sure.