Magento Zend Cache Bug

A quick one
Symptom
The Magento cron job, set up for the user running the webserver, is not running correctly besides everything seems to be configured correctly.
When you run the script as root:
bin/sh /var/www/–whatever-path–/web/cron.sh
everything is fine, but when you run the cron script being the server user:
su www-data
bin/sh /var/www/–whatever-path–/web/cron.sh
You get an error message:
PHP Fatal error: Uncaught exception ‚Zend_Cache_Exception‘ with message ‚cache_dir „/var/www/–whatever-path–/web/var/cache“ must be a directory‘ in /var/www/–whatever-path–/web/lib/Zend/Cache.php
Even when the directory exists!
Solution
I did not find a single post in the wide wide web describing this problem: the var as well as the cache directory must be u+rwx AND g+rwx! Mind the x!
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