you need to chown your installation to the php user too. i.e. if your user is www-data and they're a member of www-data you'd do
$chown -R www-data:www-data /var/www/wp-content/uploads/sites/

Try adding the user that owns /var/www/wp-content/uploads to the www-data group and chmod uploads to 775:

usermod -a -G www-data youruser
chmod 775 /var/www/wp-content/uploads

I'm still very new to this and ran across this same problem. I set up LAMP on my Ubuntu 12.10 server using the tutorial, virtual hosting with Apache2 again using the tutorial and then installed Wordpess, pointing it towards the Apache2 virtual host that I had setup. I ran into this same bug, and tried to use what you all suggested without any success.

Initially, it told me I didn't have the permissions to do that, so I tried to log in again into my root account (which I didn't disable) and it did not give me the error message, but also did not fix my problem. I tried restarting the servers, but the problem has persisted.

Anything else I can try? or any particular Apache2 config file I should look at to see if my changes are doing anything? Thanks in advance!

@a.single.drop: What's the output of these commands?

1. ps wwaux | grep apache
2. stat /path/to/wp-content