Well, the problem with my client is solved. There was a trailing slash in a path in the config.php file. Changing that into a single one solved the problem with that site anyway.
Changing
define('WB_PATH', '/var/www/vhosts/domain.com/httpdocs/');
into
define('WB_PATH', '/var/www/vhosts/domain.com/httpdocs');
solved it.