He asked people who criticized his government to prove that democracy can eliminate corruption.
Nobody ever claims as such.
I think he made it up. However, democratic government can accommodate problem solving much better than the totalitarian or dictatorial ones. Because in democratic government people are participating in the government processes freely and are not afraid of being prosecuted when criticizing their government wrong doing. This country economical and political success is the envy of the world over. People are dying to get in to this country, Lao people from Japan included.