A string of anecdotes of "I double-checked and it turned out the doctor was wrong" remains less than a trickle compared to the flood of patients doctors have to deal with, and a tiny fraction of the hypochondriacs they must deal with. Our medical system is broken enough without adding doubts on the competence of its medical professionals.
By all means, people should double-check what the doctors say, but realize the much worse consequences of sowing doubt.