I don't see how that negates the action of sending of troops for combat. You're just arguing an excuse as to why congress wasn't sought to to declare war in this "case where the President decid[ed] to send troops." There is always some excuse for that nowadays, quite conveniently, so you're in good company.

Civil war is always an exception because of the special circumstances. Its not an act of war but a state of emergency which has it's own protocols regarding presidential powers.