B for me too.
We need to find the option which supports the conclusion that patients who do not feel ill, should not go for medical checkups.
(B) Sometimes unnecessary medical tests cause healthy people to become ill. Yes, because this happens, healthy people should avoid unnecessary checkups.
(E) Physicians can eliminate the need to order certain tests by carefully questioning patients and rejecting some possibilities on that basis.
The passage states : "...It is difficult for physicians to judge exactly how thorough they should be. Therefore, it is generally unwise for patients to have medical checkups when they do not feel ill." The decision is to be made 'by the patients'. Therefore, the option is incorrectly directed.
"Always....Read between the lines"