As a physician, I agree with you that learning good people skills is a critical skill for most physicians. However, I think the whole situation is more complicated than you seem to acknowledge. First, there can be technically incompetent physicians who miss diagnoses or prescribe outdated treatments, but they're loved by their patients. On the other hand, I know a few technically excellent surgeons who are total jerks. So I agree with you that people skills and clinical skills are not totally separate and distinct, but they're not totally inseparable either. However, technical incompetence is a more serious problem than poor people skills. I agree, a doctor with poor people skills will never be truly excellent. But a technically incompetent doctor kills people.
A second, more subtle, issue is that sometimes being a good doctor requires you to do things that will make your patient unhappy. For example, a good primary care physician will bug his/her patients to quit smoking and lose weight. Those are things that annoy people, and I can tell you from first-hand experience that sometimes it's easier to make the patient happy than it is to do the right thing and come off looking like a bad guy. For example, people come in all the time demanding antibiotics for viral upper respiratory infections. Giving those patients antibiotics is doing them a disservice, as it breeds resistant organisms, but doctors that do it will be more popular, and primary care physicians do it all the time for that reason. Another example is building false hope in patients with a poor prognosis. As far as I'm concerned, that sort of pandering is cowardice pure and simple, but physicians are human too, and it's hard to be the bad guy.
Finally, posting random stuff on a web site is just not a reliable way to evaluate anyone. Mostly you'll just get a few posts from a tiny, disgruntled fraction of the patients a doctor sees. And in most of those cases, the complaint says more about the patient than the doctor. In fact, having more complaints most likely reflects the fact that the doctor is willing to accept more difficult patients, the same way that many surgeons with low success rates are the ones willing to accept the toughest cases. I agree that it's silly to try to make patients sign agreements that they won't post online, but it's even more silly to take online posts seriously.