Ok the reason I brought this up is that honestly there's probably a lot of testing that has to get done before the military would even consider coming to your backyard (or inviting you to there's) to show off your new robo-gun.
In a nutshell what I see here is a really fancy RC Helicopter, some really fancy RC aiming devices, a $50 pen camera and receiving equipment for the controller, add on a mount for the gun, replace the trigger with a solenoid, and then you have a rudimentary version of what they built. Honestly that version is not very expensive, technically complicated, or illegal to buy parts of and piece together. Additionally mapping the digital inputs from a 5vdc controller (such as the Xbox, PS3, or ancient NES) is not hard to do if you have some programming knowledge for something like an Arduino.
What I'm saying here is to get a very simple and unstable version of what they are doing is quite easy for someone with engineering background. If you can afford to purchase and shoot an AR-15 with a Trijicon, you've probably spent more on the gun than this project would cost you using a budget .22LR rifle for proof-of-concept so I think cost isn't too difficult.
So I'm guessing in order to actually test this stuff you need either a very big backyard, something on the order of a thousand acres, or a friend in the federal government to make the ATF believe you aren't crazy.
Oh and in response to this:
Name one thing that could go wrong with attatching a shotgun to a remote control car and then coming up with a way to fire the shotgun (also by remote).
The engineer decides to use a common RC Frequency such as 49mhz and gets interference resulting in an accidental discharge while he's working on the car with the gun loaded (because it was just a quick tweak) and also pointing at the front of his pelvic area.
