I get what you're saying, Mark, but my point was simply that their method of training does not neglect aerobic conditioning.
From Wiki:
Muscles trained using anaerobic exercise develop differently compared to aerobic exercise, leading to greater performance in short duration, high intensity activities, which last from mere seconds up to about 2 minutes. [ 1 ] [ 2 ] Any activity after about two minutes will have a large aerobic metabolic component.
Many CF workouts are in the neighborhood of 20 minutes (though it can vary greatly by WOD). Twenty continuous minutes of intense activity. While it's true CF isn't an endurance-focused program, if you perform it (or similar training) for an 8-12 week period and you don't achieve a significantly higher level of aerobic conditioning than a typical weight-lifting program (pure anaerobic), there's something amiss.
Give one of those 20 min workouts a shot. Granted, if you have to take a break every 30 seconds because the arms or legs fail first, then it clearly changes the whole dynamic of the workout. But once you build up the strength/endurance to keep moving continuously through the whole WOD, your respiratory system and cardiovascular system will be taxed the full 20 minutes.
I'm not saying CF is for everyone and I'm not saying it's the most effective way to prepare for a marathon or ... raise IQ. But it certainly doesn't neglect "aerobic stuff" either.
Plus it raised my IQ eight points over three months. Now I'm a 79!