That doesn't seem to be the case at all. The CoD declaration contained a list of constitutional breaches by Allende presented to the "President of the Republic, Ministers of State, and members of the Armed and Police Forces" to inform them of the "breakdown of the legal and constitutional order of the Republic." The declaration then invoked the constitutional oath taken by those parties to restore the constitution. Allende was given the opportunity to do so, but the same oath also bound the military if he did not. Pinochet's action was dictated by his oath. The point of the CoD declaration was to list the charges and invoke that oath as a basis for arresting Allende should he not come back into compliance with the constitution.
But then, I don't have a copy of the Chilean constitution on hand. Perhaps you do. Feel free to point out where the lower house resolution acquired constitutional legitimacy.