Then the point stands, as you clearly agree that the players in that situation are active. Saying "not active in a way we are using as a metric to award points" is basically you using the word incorrectly. Those are just a lot of words to simply say that achievement hunters will get more points. The metric, after all, is as you said achievements. Therefore, since you agreed that the players are active, but not active in getting achievements, we can conclude the points are not really based on true activity, but really just achievements.
Which was my point to begin with. Hence, as the first person said, you should call them achievement points and not points based off of activity. You're literally redefining the word activity to only include achievements, which it isn't.