Editing Custom Post Type's Custom Taxonomy w/ custom Role

add_action( 'init', 'tcb_create_profession_taxonomy', 0 );
function tcb_create_profession_taxonomy(){
  $labels = array(
    'name'              => _x( 'Professions', 'taxonomy general name' ),
    'singular_name'     => _x( 'Profession', 'taxonomy singular name' ),
    'search_items'      => __( 'Search Professions' ),
    'all_items'         => __( 'All Professions' ),
    'parent_item'       => __( 'Parent Profession' ),
    'parent_item_colon' => __( 'Parent Profession:' ),
    'edit_item'         => __( 'Edit Profession' ),
    'update_item'       => __( 'Update Profession' ),
    'add_new_item'      => __( 'Add New Profession' ),
    'new_item_name'     => __( 'New Profession Name' ),
  );

  register_taxonomy( 'profession', array( 'professions' ), array(
    'hierarchical' => false,
    'labels'       => $labels,
    'show_ui'      => true,
    'query_var'    => true,
    'rewrite'      => array( 'slug' => 'profession' ),
    'capabilities' => array(
      'manage_terms' => 'manage_professions',
      'edit_terms'   => 'edit_professions',
      'delete_terms' => 'delete_professions',
      'assign_terms' => 'assign_professions'
    )
  ));
}

add_action('init','tcb_create_people_posttype');
function tcb_create_people_posttype() {
  register_post_type( 'people',
    array(
      'labels' => array(
        'name'               => __( 'Peoples' ),
        'singular_name'      => __( 'People' ),
        'add_new'            => __( 'Add New People' ),
        'add_new_item'       => __( 'Add New People' ),
        'edit_item'          => __( 'Edit People' ),
        'new_item'           => __( 'Add New People' ),
        'view_item'          => __( 'View People Profile' ),
        'search_items'       => __( 'Search Peoples' ),
        'not_found'          => __( 'No Peoples found' ),
        'not_found_in_trash' => __( 'No Peoples found in trash' )
      ),
      'public'               => true,
      'supports'             => array( 'title', 'thumbnail', 'editor', 'author' ),
      'capability_type'      => array( 'people', 'peoples' ),
      'menu_position'        => 3,
      'rewrite'              => array( 'slug' => 'people' ),
      'taxonomies'           => array( 'profession' ),
    )
  );
  flush_rewrite_rules( false );
}

add_action('admin_init', 'tcb_update_person_role_capabilities', 0);
function tcb_update_person_role_capabilities(){
  if( 'person' == $_GET['remove_role'] ){
    remove_role('person');
    error_log('role removed');
  }

  $rolecaps = array(
    'read'                 => true,
    'upload_files'         => true,
  );
  add_role( 'person', 'Person', $rolecaps );
  error_log('role added');

  $person =& get_role('person');

  // CPT People
  $person->add_cap('edit_peoples');
  $person->add_cap('publish_peoples');
  $person->add_cap('edit_others_peoples');
  $person->add_cap('read_people');
  $person->add_cap('read_private_people');
  $person->add_cap('delete_people');
  $person->add_cap('delete_others_people');

  // Levels
  $person->add_cap('level_0');
  $person->add_cap('level_1');
  $person->add_cap('level_2');

  // CTax Profession
  $person->add_cap('manage_professions');
  $person->add_cap('edit_professions');
  $person->add_cap('delete_professions');
  $person->add_cap('assign_professions');

}