I'm not sure that's true. Why would the employer (who has paid for the travel through which the miles/points were earned) have to pay taxes to accept/keep the miles/points earned in the process?

What you may be thinking of is the ruling that if the employer doesn't keep them but instead allows the employeee to collect and use them, the miles/points are not taxable to the employee (unless he converts them to cash somehow). That's an entirely different situation.