Is the Multisite setup information wrong?

After switching to multisite buy following the instructions at Create a Network I do an “Error establishing database connection”.

After searching, and finding this post Database error after installing multisite, one guy said you need to include:

define('MULTISITE', true);

I added that line and now it works just fine. That is, my config now contains:

define('MULTISITE', true);
define('WP_ALLOW_MULTISITE', true);
define( 'SUBDOMAIN_INSTALL', false );
$base = '/~chris/wptestenvir/';
define( 'DOMAIN_CURRENT_SITE', 'chris-howards-imac.local' );
define( 'PATH_CURRENT_SITE', '/~chris/wptestenvir/' );
define( 'SITE_ID_CURRENT_SITE', 1 );
define( 'BLOG_ID_CURRENT_SITE', 1 );

However, that instruction is nowhere in the “Create a Network” instructions.

Is the fault in the documentation or in WP itself? Or is it something else?