There are three things that determine who can become a "great" runner (in no particular order):
1) Natural talent
2) Hard work
3) Recovery ability
If you lack any one of these, you are limited to being a
"good" runner. Talent is obvious, and hard work includes all mental aspects of training, dedication, and racing. Recovery is on this list because the best athletes have the ability to recover very quickly from hard efforts and hit it again, sometimes the next day.
I don't think recovery is as hard-wired as talent. I used to take longer to recover, but when my weekly mileage climbed from 30 to 80+ I got much quicker at recovering. The body adapts! So I don't think you can tell who is going to be great by recovery ability, but it is a good asset to have.
Recovery can depend a great deal on training too. If you are working too hard in between hard efforts or doing higher mileage than you can handle, it will slow your recovery. Notice how a lot of milers who do crazy-intense workouts cut their miles DRASTICALLY as the hardest part of the season's training begins.