I agree with the whole "don't judge a book by it's cover" bit. But it looks like that doctor is doing exactly what most would be, and that is covering up his tattoos when he's at work.
I just got a forearm tattoo. Something that I've wanted to do for years and years, and finally just said "screw it, i'm doing it." I've been in the same company for years, and am very respected for the work I do. Our divisional vp was one of the first to receive the pics from me via text, and he loved it.
However, if I was in a meeting with higher ups that I did not know, I would roll my sleeves down. Pretty simple.
My wife, who is not a tattoo person, but doesn't mind mine, asked me once how a forearm tattoo would help my fare in a job interview. I responded that the fact I was wearing a short sleeve shirt to a job interview would probably hurt me more. It was sarcasm, as I would always wear a suit to a job interview, and no one would see it.