I found this too... had to set up a default list, the search component doesn't seem to work on core CB search fields unless a list is set up and published, and then permissions open to just about everyone.
I am also finding that the same search term placed in different search fields gives the same result, regardless of which field it is in. Almost like every field is sometimes a 'search all' field?
If this component overrides the ability to specify which fields registered and non-registered users can search by and view, seems to defeat the object?
But it's a start and many thanks for all the efforts at getting this much needed component on the road.