I don't think statistically there is any evidence or history that shows an increase in AD's among experienced firearms handlers who carry with a round chambered in rifle shotgun or handgun.

The key word would be experienced.

Experienced in the manual of arms of their firearm.
Experienced so even their reloads are proper spec and done well.
Experienced so they maintain their firearms in proper working condition.
Experienced in knowing when the firearm needs to be loaded or unloaded due to the situation and HOW to properly do that and 'verify' empty 'safe'.
Experienced in muzzle control..identification of target.

I think statistically there are far more 'accidents'... AD's and shootings ....by INEXPERIENCED firearms handlers who thought or assumed the firearm was unloaded and acted recklessly..carelessly .. at odds with safe general firearms handling.

Far more accidental field condition shootings because the shooter failed to control his muzzle, be aware of non targets forward of his shooting position, failed to properly ID the target..
While I agree that a TRULY unloaded firearm is the safest..hunting ( not walking in the woods or traveling on a quad or pickup or busting brush) REQUIRES the firearm to be loaded..else one is akin to what one poster said when he remarked that 'fishing' requires the line-bait-hook to be in the water..:)and just toting a fishing rig isn't 'fishing'..

IF the shooter-hunter conducts himself well while hunting knowing that... despite the mech safety on or off, his weapon is ready to kill, he should be mentally and physically prepared to exercise best diligence and safety.

I am NOT promoting chambered carry for the hunter in general..
In fact, there are folks who have no business in the woods handling a firearm whether hot or not..

Nor am I advocating empty carry while hunting.
Prove your own methods with cognizance of your abilities and the situation and be safe..Jim