I believe he's pointing out, accurately, that wealthy families in Pakistan can be just as privileged as middle-class Americans. He's saying it's unfair to use this girl as an example of those actually living in under-privileged poverty conditions in Pakistan.
It's a fair objection, though rather emotionally contentious given the context.
Pakistani women are still not as privileged as men. Even if you were to compare a wealthy Pakistani family to some sort of American class (which would be very hard, since you would be ignoring both cultures), she would still be notable for being a 9 year old girl who became a MCP.
I think the point that it's more about the notions of the wealthy family than of the girl. Wealth allows families to transcend or disregard social norms. In this case it is clear that her family chose to raise her a particular way, and give her particular opportunities that, as you point out, would not be available to most Pakistani women.
This is precisely the point raised above, that this story is primarily about the opportunity provided by the family. But you are right, it's important to note that her family was evidently both wealthy and progressive.
It's a fair objection, though rather emotionally contentious given the context.