That's true for the part about identification and the decision to shoot it down, but in the BBC documentary (filmed on board by the navy) if I remember correctly you can clearly see how many times they failed to get an SM2 airborne from much further out than the final launch range.
"In fact, when he was finally given the green light to fire upon the incoming aircraft, he pressed the wrong keys 23 times, until a veteran petty officer leaned over and hit the right ones. Nerves were shattered, and the training seemed nonexistent.
"