I think this is exactly the case. I do remember reading that early versions of SIOP were designed to be easily triggered by a heavily compromised administration

I think this is exactly the case. I do remember reading that early versions of SIOP were designed to be easily triggered by a heavily compromised administration after an attack, so there wasn't any real room for options which would require a more complicated and confusing command protocol than just saying, "go". Command and Control (I think) touches on the back-and-forth evolution with SIOP between the various branches of military and civilian leadership.