And all of the sudden a US trained general takes over and gives the American companies back what they took from the people. Not very Democratic, not very free.

Eh? First, Pinochet wasn't trained by the US though many officers under him were (as they were all over LATAM). Second, the coup didn't happen because of nationalization. The US certainly tried to prevent Allende getting into power in 1970, however following the Schneider incident they gave up direct coup attempts and settled on level level agitation.

In Chile kennecot mines were about to be nationalized by the democratically elected Allende government.

The extent that Allende can be described as a democrat was that he was elected in a democracy; once in power he smashed the separation of powers, broke the constitution, and operated as if he had a huge democratic mandate - despite being elected by 36% of the public and supported by less than 40% of Chile's democratically elected officials. And this is what ultimately led to Pinochet's coup, Allende polarized and destabilized the fabric of the Chilean democratic, economic, legal, and social systems to such a great extent that a coup was pretty much inevitable.

There are plenty of other things you can put the blame on capital for, but Chile ain't it.