Oh, it turns out that complex exponentials are the eigenfunctions of linear time-invariant systems, and sound transmission is full of linear time-invariant systems. So surely ears cannot be perfectly detecting sinusoids, but there's a lot of evolutionary pressure to come as close as possible. That way, you can still recognize a birdsong or the howl of a wolf even if it echoes off a cliff, or recognize your baby crying even if it is facing the other way.