[lacker]

We can pick up recognizable signals only from civilizations that have worked out electromagnetic theory but have not yet developed information theory.

Really we are more likely to pick up recognizable signals from civilizations that are intentionally trying to contact us. It's possible we could pick up radio leakage, but the signal would be a lot weaker. So there are orders of magnitude more stars that could be intentionally contacting us, vs accidentally leaking a signal. (At least assuming the ratio of the strength of their intentional vs accidental radio emissions is similar to ours.)