But is the whole country absurdly wealthy? A rich ruling class might not be large enough to offset the numbers.

In the cases I can think of the whole country is rich, but they have a large number of slave-workers. Not sure if the slave-workers are counted in their health statistics or just seen as property anyway.

Or the slave-worker are foreigner, from Philipines or India, so are not counted in the national health statistics

All of them are foreigners Half of Dubai is Nepalese.

There's nearly 200000 Filipinos in Qatar