The key flaw in the Fermi paradox is that it assumes that aliens are stupid.
You would have to be stupid to disclose your existence to dangerous and hostile apes.
That is why I call SETI the Search For Extraterrestrial Idiots
The correct way to search for real extraterrestrial intelligence is the approach Professor Avi Loeb (Harvard Astronomy) is using with Project Galileo.
As telescopes get better and better his team is looking for artifacts (physical structures) of old alien civilizations on planets.
In most cases there is no practical way for aliens to hide those.