This seems odd to me. I can't install software using the "friendly" GUI tool unless I input the root password but by default, my Ubuntu 12.04 has root disabled with no password set.
Why doesn't Software Centre use a SUDO credential? Perhaps using gksudo?
This happens (at least on 14.04 which I've just tested on) when there are no users in the "sudo" group.
It doesn't matter if your user is explicitly listed in the /etc/sudoers file or not as to this behaviour -- it looks for members of the sudo group and requests a password for one of those users. If there are no members in that group then it requests the root password, which may not be enabled at all.
Edit: This is probably because the sudoers file is unreadable by normal users, but the list of members in the sudo group *is* possible to access.
