Two athletes with the same physical potential: same power, same strength, same absolute speed can score very, very differently in agility tests. Agility is a skill like swinging a golf club. I can have better balance, leg stength, hip and thoracic mobility than you, but if I don't know how to swing a golf club and you do, we both know who'll hit the ball longer and straighter.
With that said, using agility drills and equipment are going to improve performance - in those drills. You don't have to teach a thing. Sticking to the golf analogy, there's a good chance that I'll get better with time strictly due to practice. The obvious point is just because I got better at golf doesn't mean I'm swinging correctly or more importantly, safely. The same goes for agility.
Quick athletes are not just quicker. They're not just more explosive. They're not just stronger, and they're not just better conditioned. The best athletes, whether taught or not, are usually better at one thing: arranging their legs and feet underneath their torso in order to accelerate and decelerate in and from every direction. This ability is not innate, it's a learned skill. I doubt Barry Sanders ever worked with a speed guru when he was a kid, but somewhere along the line, his body figured out how to start and stop better than most athletes, ever. More to come..