The register_post_type() function takes a post type name as argument for map_meta_cap, where the default is post. Take a look at the internals of get_post_type_capabilities() for extended insights. That should help you to understand how it's meant to be:
function get_post_type_capabilities( $args ) { if ( ! is_array( $args->capability_type ) ) $args->capability_type = array( $args->capability_type, $args->capability_type . 's' ); // Singular base for meta capabilities, plural base for primitive capabilities. list( $singular_base, $plural_base ) = $args->capability_type; $default_capabilities = array( // Meta capabilities 'edit_post' => 'edit_' . $singular_base, 'read_post' => 'read_' . $singular_base, 'delete_post' => 'delete_' . $singular_base, // Primitive capabilities used outside of map_meta_cap(): 'edit_posts' => 'edit_' . $plural_base, 'edit_others_posts' => 'edit_others_' . $plural_base, 'publish_posts' => 'publish_' . $plural_base, 'read_private_posts' => 'read_private_' . $plural_base, ); // Primitive capabilities used within map_meta_cap(): if ( $args->map_meta_cap ) { $default_capabilities_for_mapping = array( 'read' => 'read', 'delete_posts' => 'delete_' . $plural_base, 'delete_private_posts' => 'delete_private_' . $plural_base, 'delete_published_posts' => 'delete_published_' . $plural_base, 'delete_others_posts' => 'delete_others_' . $plural_base, 'edit_private_posts' => 'edit_private_' . $plural_base, 'edit_published_posts' => 'edit_published_' . $plural_base, ); $default_capabilities = array_merge( $default_capabilities, $default_capabilities_for_mapping ); } $capabilities = array_merge( $default_capabilities, $args->capabilities ); // Post creation capability simply maps to edit_posts by default: if ( ! isset( $capabilities['create_posts'] ) ) $capabilities['create_posts'] = $capabilities['edit_posts']; // Remember meta capabilities for future reference. if ( $args->map_meta_cap ) _post_type_meta_capabilities( $capabilities ); return (object) $capabilities; }