Index: wp-includes/rest-api/fields/class-wp-rest-meta-fields.php
===================================================================
--- wp-includes/rest-api/fields/class-wp-rest-meta-fields.php	(revision 38842)
+++ wp-includes/rest-api/fields/class-wp-rest-meta-fields.php	(working copy)
@@ -93,7 +93,6 @@
 	 */
 	public function update_value( $request, $object_id ) {
 		$fields = $this->get_registered_fields();
-
 		foreach ( $fields as $name => $args ) {
 			if ( ! array_key_exists( $name, $request ) ) {
 				continue;
@@ -125,7 +124,8 @@
 	 * @return bool|WP_Error True if meta field is deleted, error otherwise.
 	 */
 	protected function delete_meta_value( $object_id, $name ) {
-		if ( ! current_user_can( 'delete_post_meta', $object_id, $name ) ) {
+		$meta_type = $this->get_meta_type();
+		if ( ! current_user_can( "delete_{$meta_type}_meta", $object_id, $name ) ) {
 			return new WP_Error(
 				'rest_cannot_delete',
 				sprintf( __( 'You do not have permission to edit the %s custom field.' ), $name ),
@@ -133,7 +133,7 @@
 			);
 		}
 
-		if ( ! delete_metadata( $this->get_meta_type(), $object_id, wp_slash( $name ) ) ) {
+		if ( ! delete_metadata( $meta_type, $object_id, wp_slash( $name ) ) ) {
 			return new WP_Error(
 				'rest_meta_database_error',
 				__( 'Could not delete meta value from database.' ),
@@ -155,7 +155,8 @@
 	 * @return bool|WP_Error True if meta fields are updated, error otherwise.
 	 */
 	protected function update_multi_meta_value( $object_id, $name, $values ) {
-		if ( ! current_user_can( 'edit_post_meta', $object_id, $name ) ) {
+		$meta_type = $this->get_meta_type();
+		if ( ! current_user_can( "edit_{$meta_type}_meta", $object_id, $name ) ) {
 			return new WP_Error(
 				'rest_cannot_update',
 				sprintf( __( 'You do not have permission to edit the %s custom field.' ), $name ),
@@ -163,7 +164,7 @@
 			);
 		}
 
-		$current = get_metadata( $this->get_meta_type(), $object_id, $name, false );
+		$current = get_metadata( $meta_type, $object_id, $name, false );
 
 		$to_remove = $current;
 		$to_add = $values;
@@ -187,7 +188,7 @@
 		// once.
 		$to_remove = array_unique( $to_remove );
 		foreach ( $to_remove as $value ) {
-			if ( ! delete_metadata( $this->get_meta_type(), $object_id, wp_slash( $name ), wp_slash( $value ) ) ) {
+			if ( ! delete_metadata( $meta_type, $object_id, wp_slash( $name ), wp_slash( $value ) ) ) {
 				return new WP_Error(
 					'rest_meta_database_error',
 					__( 'Could not update meta value in database.' ),
@@ -196,7 +197,7 @@
 			}
 		}
 		foreach ( $to_add as $value ) {
-			if ( ! add_metadata( $this->get_meta_type(), $object_id, wp_slash( $name ), wp_slash( $value ) ) ) {
+			if ( ! add_metadata( $meta_type, $object_id, wp_slash( $name ), wp_slash( $value ) ) ) {
 				return new WP_Error(
 					'rest_meta_database_error',
 					__( 'Could not update meta value in database.' ),
@@ -217,7 +218,8 @@
 	 * @return bool|WP_Error True if meta field is updated, error otherwise.
 	 */
 	protected function update_meta_value( $object_id, $name, $value ) {
-		if ( ! current_user_can( 'edit_post_meta', $object_id, $name ) ) {
+		$meta_type = $this->get_meta_type();
+		if ( ! current_user_can(  "edit_{$meta_type}_meta", $object_id, $name ) ) {
 			return new WP_Error(
 				'rest_cannot_update',
 				sprintf( __( 'You do not have permission to edit the %s custom field.' ), $name ),
@@ -225,7 +227,6 @@
 			);
 		}
 
-		$meta_type  = $this->get_meta_type();
 		$meta_key   = wp_slash( $name );
 		$meta_value = wp_slash( $value );