Is there any reason to think, that if there were many alien civilizations in our galaxy capable capable of radio transmission, that we would be have picked up on the signal? The last I checked (and I admit it has been a few years), the folks at SETI have basically said that even if the Milky Way galaxy was rife with technologically advanced civilizations the chance that we would have observed one is very small, given current efforts to date.
I've read a paper which pretty much lays out exactly the argument you describe, and the whole time I couldn't help but think the author was ignoring the very obvious. We can't even be sure that advanced civilizations would use radio that much, if at all, and even if they did, it's not as though we've conducted such a thorough search that we can confidently say "nope, no radios here". Not even close, in fact.