They'd have to not just be trapped in their system, but trapped on their planet. If we could get things into space cheaply, in a billion years, there wouldn't be a spot in the galaxy that a species could discover the radio and not also proof of extraterrestrial life (us). We wouldn't even need lunar colonies to do it either, let alone extrasolar ones.

I think the best argument so far is that we're just early. Supposedly, Earth is one of the earliest of the terrestrial planets to form in a habitable zone. If only a tenth of all of our type of planet produces intelligent life, we could be the very first in the galaxy. That means the only evidence of alien life would have had to cross an intergalactic void, which is a much higher hurdle.