Honestly, I thought you were one of those "republic not a democracy" people. You'd think someone who understands the meaning of republicanism would understand whether or not the lower house of the chilean legislature had the constitutional authority to call for a military coup.
You persist in holding the mistaken belief that, at the time of Pinochet's coup, the Chilean constitution was still functioning. Remnants of it were still functioning in the legislative and judicial branches, but those remnants were being forcefully overrun and ignored by Allende. By invoking the constitutional oath as a basis to arrest Allende they were invoking the doctrine of self preservation. Western legal tradition has long recognized that no constitution is a suicide pact, meaning an affirmative action that is procedurally unaccounted for in a constitution's text (note that the arrest of Allende was not barred by the Chilean constitution either though) may nonetheless be a constitutional act when it is necessary to save that constitution from complete destruction. The Chamber of Deputies' recognized that, and the strong endorsement of the coup given by virtually all non-Allendist officials in Chile served to affirm it.