Are elliptical trainers really less likely to cause knee injuries than treadmills?

Hard to say. Neither is associated with a higher risk of knee injuries. You should use equipment that you feel most comfortable with.
Yes. Treadmills allow you to run in place. The same type of impact occurs with every step as it does when running regularly. On an elliptical, the foot stays in position and there is no impact to the knee, only a smooth flexion and extension movement.
Less tripping chance. Elliptical trainers allow your feet to maintain contact with the machine throughout the exercise, whereas a treadmill mandates repetitive lifting and planting of your feet throughout the gait cycle. You are less likely to trip or catch an edge of your shoe on the elliptical trainer. When recovering from a knee injury or surgery, an elliptical trainer is initially safer than a treadmill.