The arguments over the meaning of "single action" and "double action" seem to go on forever. Unfortunately, we've created a situation in which logic conflicts with established usage, so the squabbling will likely continue for some time.
It's possible that the term "double action" arose to describe revolvers that could be cocked in two different ways, by thumbing back the hammer or by pulling the trigger. But if we were to apply this definition rigorously, wouldn't we have to classify a revolver with an internal hammer or a bobbed hammer as "single action", since it would present only one option for cocking the hammer?
Applying the definitions to autopistols gets even trickier. Look at all the permutations we'd run into if we were to classify them according to the options for cocking the firing mechanism (hammer or striker):
First, we'd have three basic cocking mechanisms: the trigger, the slide or bolt, and external levers such as a hammer or the frontstrap of a HK P7M8.
Then, for each of the three mechanisms, we'd have to decide if its operation was sufficient, or necessary, or both necessary and sufficient or irrelevant as a method to cock the pistol.
This would give us eleven possible permutations. (Three mechanisms multiplied by four possibilities yield twelve permutations, but we can safely discard the "irrelevant/irrelevant/irrelevant" combination since such a pistol could never be fired.)
Examples:
A Colt Government Model would be an "ISS", since it's impossible to cock by squeezing the trigger but manipulation of either the slide or the hammer itself is sufficient to cock it.
A Glock 17 would be an "NNI", since movement of both the slide and the trigger is necessary to fully cock the striker and there's no other way to do it.
A Beretta 92FS would be an "SSS", since either pulling the trigger, cycling the slide or thumbing the hammer will suffice to cock it. Or perhaps it would be an "SSS/III", since activation of the decocker/safety lever will make it impossible to cock by any means.
Hmmm...
Then again, there's little rhyme or reason to the way cartridges are named, so why should handgun designs be any different?