You might see funny numbers if things aren't on the display list yet. Note that Flex keeps the entire app off the displaylist until applicationComplete
Flex SDK Developer
Adobe Systems Inc.
I figured out what is happening. The base size of the sprite container is controlled strictly by the size and position of its children. When you set the width and height parameters of the container, it increases or decreases in size by changing its scale factor. So if you give it a width that is 50% bigger than the base width, all of the children will be scaled to be 50% bigger. I need to absolutely position my objects like a Canvas component lets you do, but Canvas will only accept objects inheriting from UIComponent.
So, I wrote my own class that inherits from Sprite. I gave it a method setSize which takes a width and height. setSize takes a Shape object and draws a rectangle from (0, 0) to (width, height). This sets the size of the container to width x height, so that I can then absolutely position other children within this space. I had to override all of the functions that deal with indices and counts of children so that I could add or subtract 1 as appropriate so that the external code does not need to know about the child shape that has been added. Now everything is working well.