This is a topic of considerable debate. From data collected, it does not appear that athletes injure the nondominant leg more often than the dominant leg.
One group of researchers specifically looked at how stiff the knee becomes when the muscles around the knee contract. This knee stiffness reduces the force against the ligamentd inside the knee and prevents injury. In this study, there did not appear to be any difference in knee stiffness or muscle strength between the dominant and nondominant legs.