Let's go through each of our options.
For A, the rarity of something has no effect on its validity.
For B, the study wouldn't be more valid, as you should only be testing one variable at a time (in the case, the medicine).
For C, nothing in your experiments should ever be random. And if I'm correctly interpreting it, the question means that even patients who aren't sick would be receiving the treatment, which serves no purpose at all.
Therefore, we know that D must be the correct answer, via process of elimination. Smaller sample sizes are not ideal for experiments, as they require a great deal of extrapolation to see more specific results on a larger scale.