get_post_ancestors( $page->ID ) is always empty

I’m quite stumped. get_post_ancestors is supposed to accept an integer ID, but I get no ancestors unless I pass the page object itself:

include '../wp-load.php';

$pages =& get_pages();

foreach ( $pages as $page ) {
	var_dump( $page->ID // = string "integer"
		, (bool) get_post( $page->ID ) // = bool true
		, get_post_ancestors( $page->ID ) // = empty array
		, get_post_ancestors( get_post( $page->ID ) ) // = empty array
		, get_post_ancestors( $page ) ); // = array ancestors (success)
}