@Jeffro -

So, it must be doing it a different way, perhaps storing them in the database?

Nope; filters. Specifically:

if ( 'no' == $options['active'] ) {
add_filter( 'auto_upgrader_disabled', '__return_true', 1 );
} else {
if ( in_array( $options['core'], array( 'dev', 'major', 'minor' ) ) ) {
add_filter( 'allow_' . $options['core'] . '_auto_core_updates', '__return_true', 1 );
}
if ( $options['plugin'] ) {
add_filter( 'auto_update_plugin', '__return_true', 1 );
}
if ( $options['theme'] ) {
add_filter( 'auto_update_theme', '__return_true', 1 );
}
if ( ! $options['translation'] ) {
add_filter( 'auto_update_translation', '__return_false', 1 );
}
}

(And similar filters for the update emails.)