My understanding is that Pinochet was virtually asked by the Chilean parliament to oust Allende because they saw what was coming. Namely, that Allende would follow standard communist operating procedure and start fiddling with the constitution to guarantee permanent rule by his communist party. Once Pinochet was confident that Chile's communism problem had been solved and order had been restored, he voluntarily stepped down and turned power over to an elected civilian government. Such the evil dictator, he.
I don't know all the ins and outs of Pinochet and Allende, but one very salient fact is that the Left hates Pinochet. That alone should tell you something. At the very least, it means you can expect the media to slant its telling of the history against Pinochet whenever possible.
Regardless of how much the Left hates Pinochet, I have no love for him at all. Obviously, it was good that Chile did not become a Soviet satellite because of his coup, but Pinochet was brutal despot. Allende was also bad, but Pinochet was no improvement from a human rights perspective.
I credit Milton Friedman, not Pinochet, for making Chile free. Pinochet was simply amendable enough to accept ideas for reform.