Apache www-data group write permissions to modify WordPress not working

I’m trying to give write permissions to Apache www-data group to be able to install new plugins directly from WordPress webadmin console but it seems like these permissions are ignored.
I have to give write permissions to www-data user and everything works fine. But why user and not just group?
I’m working on Debian 7.5 with LAMP (Apache 2.2, php5, MySql 5.5) stack and WordPress 3.9.1.
Wordpress folders are on /var/www/mysite and the website is managed by a virtual host:

<VirtualHost *:80>
    ServerName my.site.com
    ServerAdmin thewebmaster@localhost
    DocumentRoot /var/www/mysite
    ErrorLog ${APACHE_LOG_DIR}/mysite-error.log
    CustomLog ${APACHE_LOG_DIR}/mysite-access.log combined
</VirtualHost>

www-data group seems ok getent group www-data says www-data:x:33:www-data and file permissions too. Showing ls -l this works…

drwxrwsr-x  5 www-data www-data 4096 Jun 19 07:22 mysite

and this doesn’t (with root user as owner):

drwxrwsr-x  5 root www-data 4096 Jun 19 07:22 mysite

Any suggestions? Thanks in advance