We also have to account for demographics and understand the risk/benefit analysis. That 96% number is from a WebMD survey of about 300 physicians. The ages are mostly over 50 with only 7% being under 35. So they are in the somewhat higher risk groups. They also work a job that runs a high risk of exposure. This means they might see their risk of infection and serious illness being high enough to justify it without feeling it is necessary to recommend it to everyone. For example, we don't all receive rabies vaccines yet many animal handlers do.

Another important thing to note is that there could be bias in that group. If you dedicate your life to medicine, you may be more likely to trust medicine without questioning it. Unless you've had an experience that was negative. Many physicians that have had negative personal experiences abide by the idea that new means unproven (which matches the reason that most unvaccinated doctors gave in the survey and the CDC lists - that the longterm risks are unknown).

Lastly, most doctors are to mechanics as medical researchers are engineers. Most doctors aren't looking up studies on PubMed or doing research. They mostly rely on what they've been taught in school and in continuing education. For the most part they are following established protocols. Hell, even the experts admit that there is a lot they don't know about the immune system. Take for example that researchers are seeing protection from the vaccine before antibodies are produced - which was unexpected.

So while most groups are susceptible to misinformation, that doesn't invalidate the position that one may avoid the vaccine due to the unkmown longterm affects. It's really a question of risk/benefit analysis in a sea of incomplete information.