I think I understand what you are saying.Safety stats are heavily influenced by who takes the training. Folks that seek out training are safety conscious, more so than the average population. It follows that they will have a lower incident rate. This was demonstrated time and again by the FAA
WINGS - Pilot Proficiency Program. It was/is a voluntary ongoing safety training program. It has long demonstrated a lower accident rate by participants than the general pilot population. Is it because of the training or the mindset of those who VOLUNTARILY opt for additional training (not legally required for their license) ?
The belief is the lower accident rate has nothing to do with the training, it is a result of self selection of like minded safety conscious pilots. They might as well hold their meetings at the Pink Pony, and skip going to the airport to do them, if the same group of pilots choose to participate.
Gun owners that choose to not acquire a CCW, or take any form of instruction are not likely to benefit from mandatory training, they just aren't interested or think it is important.
Overall stats from similar States are close to the same, regardless of the reasons. However I agree with your reasoning.