expressions - What rhetorical gain is expected by saying “Do they really not understand why?” instead of “Don’t they really understand why?”

There was the following passage in the New York Times (August 14) article written by Paul Krugman under the title, “Bungling Beijing’s Stock Markets.”:

These (occasional intervention to prop up asset prices) were
short-lived actions, taken at times when markets seemed to have lost
their bearings. Staffers at the Federal Reserve used to call these
moves “slap in the face” interventions. That’s very different from the

kind of sustained intervention and political dictation of prices China
seems to imagine it can pull off. Do the country’s leaders really not
understand why that won’t work?
http://www.nytimes.com/2015/08/14/opinion/paul-krugman-bungling-beijings-stock-marketshtml.html?action

Though it may sound very naïve, I’m curious to know what difference of nuance, or artfulness of statement comes up by bringing “not” later - Do the country’s leaders really not understand why? instead of earlier - Don’t the country’s leaders really understand why?”

Is there any difference of implication or tonality between two alternative lines, or they are exactly same, and it’s simply a matter of the writer's style / taste?

Answer

Those two sentences emphasize different things, which means that in a sense they're asking different things.

Don't the country's leaders really understand why that won't work?

This puts the emphasis on understand, and is thus a straightforward question: do they or don't they understand? (Also, in this version, "really" modifies "understand", which in my mind kind of weakens the question by giving the leaders an "out": we assume they understand a little bit, and the only thing in doubt is whether they understand the issue well.)

Do the country's leaders really not understand why that won't work?

This phrasing puts the emphasis on really, and thus instead of being a straightforward question, it becomes an expression of incredulity. We're not really asking whether they understand or not, because all the evidence says they don't; instead, we're asking whether we really ought to believe that evidence. (In this version, "really" modifies "not", which is what makes this into an incredulous questioning of our own sanity, almost, rather than a query about what the leaders know or don't know.)