Guys... you're going too deep with the how's and why's of these two problems.
1st the Red Bull style crate is easier to break-down.. it's an Extra 300 type aerobatic plane... and packs a huge punch with it's massive and very capable engine. How I picked it for a lie is simple. Recovery time. There is no way in hell a human could have the ability to recover from an out of control spin like that, hang on the prop, have it level, and then cut the power so that it stops in mid-air, 20feet above the ground and drop without further damage. Impossible. The physics and aerodynamics do NOT add-up and let's not forget the strain on the human body. Any fixed wing plane, unless in a nose-up condition, will still glide forward when the engine is cut. If actually recovered, even though the Extra is extremely responisve, your brain isn't. The plane would have swayed a little back and forth as the pilot tried to regain his own bearing, let alone the HSI, and the plane itself.
2. The F15 is harder, but makes more sense. Remember the F104? It was an engine with wings and a cockpit. Basically, by jacking-up the throttle into military power, it forced the basics of aerodynamics to level itself out. Anythig will fly straight given basic stability and enogh power to push it. Ever notice when you fly a paper airplane, for the first foot or so, it's perfectly straight, then goes crazy? That's because you are overriding the poor aerodynamics with sheer power. That's how an arrow works. The pilot did something simply no other pilot thought of, that is add power. But as he slowed down, he most likely was able to get a better feel for the plane that it was missing a wing, and with the stability computers helping out, maintain control of it until he landed safely.
I dunno, sounds right to me... and add in a little... don't believe everything you see.
OvS