1152: A conflict exists with inherited definition in namespace public

I have an actionscript 3 library item, "BG", that is linked to the class BGClass. BG contains a Sprite that has an instance name, "bg" and likewise BGClass has a public bg property. So the class looks like this:

public class BGCass extends Base {

    public var bg:Sprite;

    public function BGCass() {
        bg.width = 200
    }
}

Everything works fine. But if I wish to move the public bg into the Base class like this I get the error.

public class BGCass extends Base {
    public function BGCass() {
        bg.width = 200
    }
}

public class Base extends Sprite {

    public var bg:Sprite;

    public function Base() {
    }
}

I have tried using getter setters in Base and overriding them in BGClass and I still get the error. Is this a bug in Flash? Is there a clean solution or do I need to create some sort of proxy variable to finally get bg to Base? I know that turning off "automatically declare stage instances" in Flash will get rid of the error but I need to keep it on for the designers. Any solutions?