Keep in mind that in your latter example there would be six grants awarded, which either means no quarter has exactly two grants awarded (3-1-1-1) or more than one quarter is going to have exactly two grants (2-2-1-1). Neither of these satisfies the new condition of this question.
Here's our setup for this one:
The key on this question is to recognize that only one distribution is possible (2-1-1-1). That ensures that only one of the four areas repeats, and we know which one ... medical services.
(A) cannot be true. We know that youth services will only be awarded a grant in one quarter.
(C) cannot be true. We know that wildlife preservation will only be awarded a grant in the second quarter.
(D) cannot be true. If youth services and theater arts are awarded grants in the first quarter, then both medical services grants would be awarded in the third and fourth quarters and would be consecutive.
(E) cannot be true for the same reason as (D). This would require that both medical services grants would be awarded in consecutive quarters (third and fourth).
That leaves answer choice (B), which could be true: