one was a free market fundamentalist: Pinochet
Repeating a lie often enough does not make it true.
Pinochet was resistant to free market, through most of 1974 his own style of handling economic problems left in the wake of Allende meant putting the army in charge of alleviating penuries through requisitions, rationning and distribution, and it was a complete failure. Chile kept printing money just like under Allende, leading to 300% inflation in 1974 and 1975.
If Pinochet was, as you put it, a "free-market fundamentalist", then explain why did oil and copper industries remain state-owned all through his regime, and why did the fishing and forestry industries remain syndicate-run (CORFO) ? Why did he keep in place many programs of subsidies ? Why did he have several failing corporations bailed out (like the Osorno bank) ? Why did his constitution of 1980 keep copper resources as irrevocably public property ? Why was the Peso pegged to the USD, chinese-style, in the early 80s (leading to a monetary crisis and recession), instead of maintaining a free-floating exchange rate like Friedman advocated in his speeches and books ?
Oh, right: that's because Pinochet was NOT a free-market advocate. He was not even right-wing either - his wife was a senator in the Radical Party, an ally of Allende's Unidad Popular, and he was a close collaborator of Allende until the coup d'état. Instead, his pragmatism at least let him put people who mostly were free-market enthusiasts in charge of some of his government's economic policies. He, himself, had no such convictions, he was just an autoritarian voluntarist. But I guess that makes for an insufficiently romantic narrative to convince you.
Sergio de Castro Spikula was one such free-market enthusiast in Pinochet's government, and he had to bitterly fight (there even was one incident with a gun) with other members, like General Gustavo Leigh, Admiral José Toribio (president of the government's economic committee), or Raul Saez (the man who was responsible for planning the economy of Chile in the Junta), in order to get the reforms done.