I'm working from memory here, and, yes, I agree that civil operations are as you describe. But, if I recall correctly, civil ops involve a scenario such as the 1906 San Fran Earthquake. The local Army commander immediately responded by sending his troops to help save lives and property.
The "civil disturbance" scenario is different, I think. The response to a civil disturbance, such as a huge riot or insurrection, would presumably involve using troops in police activities to restore order. This is much different from helping to put out fires and sending medics to apply bandages to the injured, so, some concern might be warranted.
I'm sure that the problematic parts of the DoD reg can be revised. I doubt that there is some secret DoD intent to expand any existing laws or policies via "stealth" regulations.
This post was edited on 5/19 at 12:11 am