The only way a rifle bullet can go three miles is if you fire it at about a 45 degree angle. Since the average deer is about 4 to 5 fee tall to miss the deer and go 3 miles would mean you couldn’t even see the deer in your scope or open sights when you fired. There is no evidence that shotgun slugs cause less accidental injuries than rifles during hunting season.
Yes, even the article acknowledges that, and it's not like they haven't been looking. As 50cal Smokepole correctly noted upthread, there's no longer any practical difference between rifle/shotgun/blackpowder in the context of the town chairman's concern.
Many types of rifle, if fired at the correct upward angle, would have lethal velocity when they hit the ground a couple miles away. Aiming at such distances would be impossible, but as has been observed, sometimes the danger isn't the bullet that has your name on it, but the one addressed "to whom it may concern".
Nonetheless, if hunters shoot from tree stands and exercise reasonable discipline such as unloading or at least opening the action when they are climbing up and down trees, I wouldn't think shots would be fired upward at angles likely to cause long range injuries.