Okay, if so, I found a bug. :D
Notifly send emails for comments on private posts. But they are also private.
Besides a suggestion: what about a filter to allow notifications for private content? I'm sure that there are more users who need such a feature and it would prevent me from forking your plugin. And forks are evil. :D
Currently I replaced the code above by:
$public_statuses = array( 'publish', 'private' );
$only_updated = in_array( $old, $public_statuses );
$public = in_array( $new, $public_statuses );
if ( $only_updated || ! $own_public ) return;