I have already asked the same question and in a 2010 Child Theme you cannot remove the Appearance > Header or Appearance > Background, which are set by the parent.
There are functions to add theme support but not to remove theme support for all theme features.
They are listed as “Extra Theme Support” but there is no function to remove support for these functions.
You can remove support for “Theme Functions”:
-> Post Thumbnails
-> Navigation Menus
-> Widgets
-> Post Formats
You cannot remove support for “Extra Theme Functions”:
-> Custom Backgrounds
-> Custom Headers
-> Editor Style
-> Automatic Feed Links
The pages are added with the function add_theme_page(), but there is also no remove_theme_page().
The only ways around this is to create a full theme and remove the header parts in functions.php.
Looking at the 3.1 beta 2 theme it is not addressed there, it would be good if WordPress added these calls to functions in the default theme so a child theme could overide these.
HTH
David