I don't think the claim that he supported Pinochet means he had a direct hand in the coup, it's that he attempted to re-engineer the Chilean economy after the CIA linked plot assassinated the democratically elected socialist president who was attempting to socialize parts of the economy. The free market reforms were a disaster for the people that were only able to be applied under the terms of dictatorship.

https://en.wikipedia.org/wiki/Salvador_Allende