Ankle reinjury depends on many factors. Ankle sprains can be mild, moderate, or severe. The more severe a sprain, the more soft tissue structures are damaged. The healing response varies from person to person with all levels of injury.
So in theory it's true that having an ankle sprain can put you at increased risk of another sprain. It's just that researchers haven't been able to predict who is at greatest risk. This makes it harder to prevent re-injury.
We do have some information that suggests rehab must include retraining the proprioceptive system. This is the mechanism in the ankle that allows it to make small changes in movement when needed. For example, if you step on a stone and need to make a sudden correction in your foot position, it's the proprioceptive system at work to do that. Preventing twists and turns of the ankle depends on this system.