The restriction is not from ispconfig. but it gets applied as you uploaded data with a different user then the one that is configured for this vhost and this user is set and configured by ispconfig.
In a ispconfig setup, every website has its own user. If you wnat all sites to run under the same user, you will have to modify the ispconfig code so that ispconfig uses the user ww-data or whatever you want to use as user for all sites. the user of the site is set in the file /usr/local/ispconfig/interface/plugins/sites_web_domain_plugin.inc.php. The interesting lines are:
$system_user = $app->db->quote('web'.$page_form->id);
$system_group = $app->db->quote('client'.$client_id);
change it to something like:
$system_user = 'www-data';
$system_group = 'www-data';
The user and group name might differ for different linux distributions.