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Exactly. Now remove the restriction that Earth #2 is active with life at the same time we are. Instead intelligent life existed 10 billion years ago. Now we've got a tiny band of space 10 billion light years away where that planet has to be located where we could have possibly detected it. It doesn't seem that unlikely that we haven't found intelligent life.

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If I had to bet on the right answer it would be this. The time scales of the universe are mind-fucking and we are just naive if we think we can maneuver around them.

The point of the paradox is that if intelligent civilization is only active for 200 years out of a 10 billion year timespan, there is something seriously wrong with the survival rates of such civilizations.

Or, they became something different, not worse. For example, Victorians would have looked silly to scan the skies for aliens by looking for soot clouds in their atmospheres, because all 'civilizations' would have steam trains.

We're looking for radio waves. Radio waves! Like a million-year-old civilization wouldn't be communicating with nano-soliton-pulse masers across interstellar distances. And to receive one of those, earth's orbit would have to accidentally cross its path, and then only for an instant. The chances are trillions to one, and we wouldn't recognize it if it happened.

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