Without a contract, the employee is employed at the will of the employer as well as himself. That is to say that neither is bound to the other. Therefore an employer may terminate an employee without cause at his own discretion. The employer can set the conditions of employment regarding the qualifications of the employee.
The inability to obtain access to a nuclear plant is not a protected class of individual unless it is the direct result of disability, race, sex, sexual orientation, religion, or veteran status.
The NRC does not regulate employment law. You could try the Department of Labor, the EEOC, or a state agency, but it won't help unless you can prove discrimination against the individual based on one or more of the aforementioned protected classes.
Keep in mind that mental illness is a disability if it negatively impacts the employee's ability to work. If there is a medical or mental condition that prevents the nuclear access of an otherwise qualified employee, the employer is required to make reasonable accommodation -- including but not limited to job transfer or reassignment. That is the only chance your guy has. If it is because of criminal history or drug use, no luck.
