Flexibility is a bit more than just flexibility. A few examples:
- Someone who does nothing but stretch and yoga. They're not very strong, but boy can they bend. They couldn't jump or sprint to save their life. Probably not getting injured for stepping off a curb anytime soon.
- Someone who only lifts through a very short range of motion, never stretches. Might be able to jump through the roof, likely at a higher chance of injury.
- Someone who squats very deep, jumps from deep squats, etc. Someone like an Olympic lifter, they have very good flexibility but have no issue being explosive.
So the yoga person wouldn't make a good runner, and the second person might make a good runner but anything "unexpected" could pose a risk of injury, something as simple as losing balance while jumping.
The reality is, you can be flexible and springy, you just have to train it. You probably don't need to be as stretchy as a gymnast, but they seem to have no problem jumping very high.