There are a few instances of Attachment-specific conditionals in the Posts controller that would be better off in the Attachments controller:

• WP-API/lib/endpoints/class-wp-rest-posts-controller.php

  Lines 537 to 539 in a93ea66

  	if ( empty( $query_args['post_status'] ) && 'attachment' === $this->post_type ) {
  	$query_args['post_status'] = 'inherit';
  	}

• WP-API/lib/endpoints/class-wp-rest-posts-controller.php

  Lines 962 to 972 in a93ea66

  	// Can we read the parent if we're inheriting?
  	if ( 'inherit' === $post->post_status && $post->post_parent > 0 ) {
  	$parent = get_post( $post->post_parent );
  	return $this->check_read_permission( $parent );
  	}
  	// If we don't have a parent, but the status is set to inherit, assume
  	// it's published (as per get_post_status()).
  	if ( 'inherit' === $post->post_status ) {
  	return true;
  	}

• WP-API/lib/endpoints/class-wp-rest-posts-controller.php

  Line 1615 in a93ea66

  'default' => 'attachment' === $this->post_type ? 'inherit' : 'publish',

• WP-API/lib/endpoints/class-wp-rest-posts-controller.php

  Line 1636 in a93ea66

  if ( 'publish' === $value || ( 'attachment' === $this->post_type && 'inherit' === $value ) ) {