MySql error a potential security risk?

Recently my web host had some down time and I got the following error from drupal with the drupal logo on it;

Unable to connect to database server

This either means that the username and password information in your settings.php file is incorrect or we can't contact the MySQL database server. This could mean your hosting provider's database server is down.

The MySQL error was: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (111).

Currently, the username is XXXXXXXXXX and the database server is localhost.

Wouldn't it be prudent not to show the username and the ip/location/name of the MySql server?