I believe it's not as big a stretch as some might imagine. Post-war Latin American [right-wing] authoritarianism took some inspiration from European fascism. To say that Chile under Pinochet didn't resemble the Iberian fascist regimes of Franco and Salazar would be an actual stretch. After the coup, Pinochet brought in a number of University of Chicago students who studied under (and idolized) Friedman; they set the economic policy of Chile for the next two decades.