Bill— The most obvious answer is that it’s a matter of intent. Being on the outside lead by accident gets you no credit. However, that heightened level of obedience to your aids which allows you to choose your lead—true or counter— ensures that your horse is not taking his lead by rote or on autopilot.
In and of itself being able to do that is a good start but only get you so far. A useful counter canter is all about your horse’s balance. Read that as promoting “longitudinal suppleness” — the ability to shift your horse’s weight forward and back without resistance, in other words, to collect him.
A counter canter without this quality is really just cantering on the wrong lead; however, being able to ride a straight and balanced counter canter through increasingly difficult exercises (like the S turns in Fourth Level test three) are a great gymnastic for your horse.
Some horses are practiced enough that they can make a pretty decent true canter by “mailing it in” without much thought or commitment. Not so with counter canter. That’s why Danish Olympic judge Colonel Aage Sommer would insist “one good counter canter is worth ten true canters.”