Messing with the armed forces or police seemed to be part of growing up as a teenage boy for some of my friends. (I was tempted to write rite of passage here but that would imply that it happened once for each.)
Of course they like me wasn't too well of so it was all about illegal fireworks, sneaking, swimming or canoeing into military or naval bases etc.
No doubt in my mind they could have tried something similar to this if they were young today and had the tech skills and money for it.
IMO, either the story as reported has been exaggerated in many dimensions (altitude above the chopper, size of drone, time in the air, distance before landing) or it's something from the air force base that's not commercially available.
And yes, you are right that I'm only talking about young people playing games with police/military and I don't have any idea if this is feasible or not.
All kinds of exciting things can get people into serious trouble but they still do it. For example, drifting and street racing expensive cars at night. Some even taunt the police. Here's a good series: https://www.youtube.com/watch?v=clf-KhniImw
In my mind flying a remote controlled drone over an air base seems way less risky than hitting the streets in a car.
I just don't think private drone is the angle here. More likely to be an experimental agency thing, and someone flying a work gadget they haven't personally paid for, IMO.