I was getting the same error and couldn't figure out the problem for ages. If you happen to be on a Linux distribution that includes SELinux such as CentOS, you need to make sure SELinux permissions are set correctly for your document root files or you will get this error. This is a completely different set of permissions to the standard file system permissions.
I happened to use the tutorial Apache and SELinux, but there seems to be plenty around once you know what to look for.
