Seeing as Pinochet wasn't named commander in chief until after July 6th, it is unreasonable to expect that Frei would have mentioned him on July 6th. What Frei did say then, however, was this:
"There is nothing that can be done by myself, by Congress, or by any civilian. This problem can only be fixed with arms. I share your apprehensions, and I advise you to state them plainly to the commander in chief of the Armed Forces, hopefully today."
Pinochet was named commander in chief a few weeks later, thus becoming the officer that Frei had endorsed to depose Allende.
Pinochet's nomination cannot transform Frei's comments ex post facto. If you have any evidence of Frei commenting on Pinochet's alleged desire to protect the Chilean constituion, please show it now. Otherwise, you were caught claiming something that is not supported by the evidence of history and you should drop the subject.