I saw your post in Jet Blast. Chasing UFO's hardly seems to be a military problem. What I gleaned from the youtube you shared is that its political stuff.
Using the Hellfire as an air to air weapon is an interesting wrinkle on that munition.
I know a little bit about Hellfire (albeit my experiences are a few decades old.)
It's an anti-tank weapon, meant (optimized) for air-to-ground attacks. In the US Navy, they modified the SH-60B (and now MH-60R) to carry and deploy the Hellfire as a lower cost anti boat/anti small ship weapon. It's original purpose was tank busting. The speed of the thing you had on the video in JB was quite a bit more than a boat or a tank. That might inform the difficulty in using Hellfire as an air to air weapon.
To make it an more effective air-to-air weapon, there would need to be a mod to the warhead so that something like a proximity fuse + HE/Blast Frag warhead is used rather than the anti-Tank / Anti-Boat warhead.
Granted, our Army and Navy have had a number of years to test out various mods to this Laser guided anti surface missile. I am not privy to any recent developments. (And there quite a few different mods to the missile).
When I was in the Middle East, Reaper had only recently come on line, but the Predator used the Laser guided Hellfires to very good effect on a wide variety of ground targets. At the time, we didn't have any TTP (Tactics, Techniques, and Procedures) for using Hellfire in an Air-to-Air mode.
There was apparently a development for a ground-to-air mode.
Suggest you head over to the Wikipedia page for the AGM 114, it's a great treatment for that munition.