From the Satellite photo you show , there is quite a bit of distance between you & where he was supposed to be when he shot . You can hear a Pellet gun when its shot next to you , but even 50 yards away you won't hear much if anything , sure there are some that have a muzzle velocity above the sound barrier & thats what can be heard , but they quickly go below it after a short distance & is hard to hear down range .
I am will trained in firearms & you would have to be well practiced at shooting at flying objects to hit a Drone at the distance that is shown in that photo , not to mention , I doubt a Pellet gun would have had that much energy to bring the Drone down , if it had enough to even penetrate the Drone's Shell , thats one hell of a shot with a projectile with a trajectory of a softball at that distance . Air pressure or even CO2 is not good for distance of any kind , sure small game & even Hogs are shot with some of the high $$ Pellet guns , but the Hogs are shot at near point blank range in the Ear canal.
The reason he probably told LE it was a Pellet gun is , as I have said , they would or should have charged him , if he used a firearm of any sort , shooting in the air is illegal . A Pellet gun is not a Firearm .
I would like to know what the FAA ruling is on these type of situations , after all they want us to Register them , there should be some kind of regulation about shooting down a registered craft of any kind .
The Police chief is an idiot & probably grew up with this Bone head .