Would you not consider it fair to say additionally that pilots who have demonstrated above-average levels of competence tend to show the traits that make up the underpinnings of CRM (whether they've been trained in CRM or not)?
No, I think I would disagree. I would think that being above-average competence is not necessary to show the traits that make up the underpinnings of CRM. The great unwashed majority of flight crew are competent. The industry problem is that the outliers are problematic, and overrepresented often, (but not always) in the funny pages. (The great majority used to be washed, but then the industry came on hard times, hot water is now a luxury, except if you have annoyed your management...). 80:20 rule.