As the parts in the skin are added by the component this gives it the power to ensure that you can't click on the graphics, if you look in ButtonBase class which Button extends you can see the comments that explain this:
// DisplayObjectContainer properties.
// Setting mouseChildren to false ensures that mouse events
// are dispatched from the Button itself,
// not from its skins, icons, or TextField.
// One reason for doing this is that if you press the mouse button
// while over the TextField and release the mouse button while over
// a skin or icon, we want the player to dispatch a "click" event.
// Another is that if mouseChildren were true and someone uses
// Sprites rather than Shapes for the skins or icons,
// then we we wouldn't get a click because the current skin or icon
// changes between the mouseDown and the mouseUp.
// (This doesn't happen even when mouseChildren is true if the skins
// and icons are Shapes, because Shapes never dispatch mouse events;
// they are dispatched from the Button in this case.)