I think that the poster's supposedly wrong answer would work fine under two conditions: (1) the poster is allowed to add a comma after "Meanwhile"; and (2) the sentence in question, rather than having fallen out of the blue, blue sky, appears in the context of a preceding sentence that says something to set up the contrast that "Meanwhile" attempts to convey.
New York City's innovative, privately operated Puppy Ambulance service caters exclusively to AKC-registered blue-blood canines in distress, for pet-loving citizens who can afford the steep fees involved. Meanwhile, understaffed and under tight budget, 911 centers are struggling to adequately provide emergency assistance to the citizens.
It wouldn't be hard to set up similar similar contexts that made the "Yet" and "But" options perfectly reasonable, as well.
I suspect, however, that the test deviser intended to set up a situation where no prior context is allowed, and where the sentence must make sense without reference to anything outside the included wording plus the optional opening word. In that case, as J.R. indicates in a couple of comments beneath the original question, "Although" is the only arguably satisfactory choice.
But the test deviser severely undercuts the sentence's independent readability by referring at the end of it to "the citizens" (rather than simply to "citizens")—as though the reader has already been introduced to these particular individuals. As devised, the sentence invites the test taker to assume that outside context exists for "the citizens" but then punishes the test taker for assuming that outside context also exists for a transitional word such as "Meanwhile" or "But." You can't have it both ways—unless you're the test deviser and you make all the rules yourself.
No wonder the poster was confused by this test question. Bad job, test deviser!