Option A - INCORRECT.
It is possible for both Ellen and Lois to right about Shirley's children if they had seen them in different time and day.

Option B - CORRECT.
Accepting the fact that nobody that has measles is fine, and in the case of Ellen claiming to have seen Shirley's children having measles is right as at the time she saw them, but as for Lois to claim that ''as a matter of fact'' that Shirley's children are fine means that, as at the time she also saw the children they were already treated of the disease and they are fine now. Therefore, It is possible that both Ellen and Lois are not mistaken about Shirley's children due to the time and scenario which they both saw the children.

Option C - INCORRECT.
Looking at the scenario, Either Ellen is right about Shirley's children, or Lois is right about them, but they both be right as at the time they saw the children.

Option D - INCORRECT.
Ellen and Lois might both be right about Shirley's children, and they might both be wrong about them. Which this claim can only be justified if the time frame at which they both saw the children was indicated in the argument.

Option E - INCORRECT.
One of these alternatives best identifies the possibilities for this scenario, which is Option D, stating that ''Ellen and Lois might both be right about Shirley's children, and they might both be wrong about them''.