Can't tab inside Scrollpane

I can’t find an answer to this. Maybe somebody here knows.

The TextFields being inside a ScrollPane seem to make tabbing not work. I tried a similar case with a Sprite instead of a ScrollPane and all works as expected. But with this test case, if you click inside a TextField, then hit <tab>, the focus goes to the whole ScrollPane, and never tabs to a TextField. OTOH, if I were to add Buttons into the ScrollPane, they would be in the tab order - but not the TextFields.

Can I make tabbing through the textfields work, inside a ScrollPane?

package {

    import flash.display.*;
    import fl.containers.*;
    import flash.text.*;

    public class SPTest extends Sprite {

        var sp =  new ScrollPane();

        public function SPTest() {
            sp.x = 100;
            sp.y = 100;
            sp.width = 400;
            sp.height = 400;

            var spr = new Sprite();

            for (var x = 0; x < 4; x++) {
                var tf = new TextField();
                tf.text = "tf" + x;
                tf.type = TextFieldType.INPUT;
                tf.border = true;
                tf.height = tf.textHeight;
                tf.y = x * 30;
                tf.tabIndex = x;
                spr.addChild(tf);
            }
            sp.source = spr;
            addChild(sp);
        }
    }
}