I agree that power lines at the low frequency they operate should not interfere with the RC/AC radio signal.
Its also true that contacting one line in general will do nothing.
But there's more to consider than loss of radio signal or making a direct path of dangerous current.
If you're close enough to the tower which is grounded when you touch a line, and the voltage is high enough, electricity can arc through the air, through the AC, and then to ground. Just Google videos of kites getting too close to the lines and see how far the electricity arcs.
Also with the high current, a strong alternating magnetic field can be generated which can mess with the compass, and also generate unwanted current in the AC circuits and motors. After all, that is how transformers work.
It's just best to stay a good distance away for many existing and potential issues, including physical, electrical and magnetic.