I wonder if this is a legitimate way to look at things: Imagine a caveman who knows absolutely nothing about mathematics or mathematical logic; i.e., he is totally incapable of rigorous deductive and/or inductive reasoning (therefore, any conclusions he reaches are based only on his eyeballing of the data, and not on his ability to derive any logical consequences).
Now, I believe if you gave this caveman a sample of several hundred positive integers selected randomly from the first, say, 1015 positive integers (far more than the number of stars in the galaxy), and he were willing to stick out his neck for his hypercritical caveman buddies to lop off his head if he is wrong about anything, he would absolutely be able to make a whole bunch of valid conjectures about the first 1015 positive integers, indeed, about all integers in general.
That's the power of sampling. It doesn't hurt us one bit that our sample is almost vanishingly small in comparison to the larger population. The only thing that matters is, is our sample representative? That's all I'm saying.
Our SETI data constitutes a very small sample relative to the larger population. But it doesn't matter. We can live with that. The only question is, is the data representative? I think there is a good chance the data are representative.
Make sense, or nonsense? :-)
How do we know we are taking the correct samples?
Most SETI searches ar at the 21cm band. We have international treaties to not broadcast at this frequency at all. So here we are looking for signs of a narrowband signal heralding the fact that intelligent life is not wholly constrained to this little dirt ball at this frequency. Now if any intelligent race develops radio and radio astronomy, they too will recognize the importance of this 21cm band. And they also may instigate a SETI search using this frequency. So here is the question. Would they hear us at that frequency? It is the one that we are not transmitting on at all. I could just see 500 races all looking for each other at the very frequency none of them are transmitting on due to the very nature of the importance of that frequency to the exploration of the universe.