Yes that might be one of the reasons why we haven't encountered any alien life but any such intelligent life must be able to find the evidence of another life capable of interstellar travel even if they're not present at the same time, don't you think? I mean there must be a lot of data and information created by intelligent life in the universe. Voyager 1 and 2 come to mind.
But yeah as you said, that is statistically very unlikely.