The far side of the moon is no more or less dark than the side we see.

It is from the Moon's perspective. On the visual spectrum the Earth is much larger and more reflective than the Moon. You're looking at something like 40x greater illumination during a 'full Earth' than you get during a full Moon on Earth. Earth is also extremely noisy in the radio spectrum for radio telescopes, while the Moon itself blocks most of all of that out on the far side.