Ubuntu – How to prevent system applications (like the Software Center) from asking for password

As already said, the problem may be your PolicyKit configuration. I would be interested in the contents of the files in /etc/polkit-1 directory and the file /usr/share/polkit-1/actions/org.debian.apt.policy. The output can be lengthy, so you may want to compress it and upload it somewhere rather than copy it here...

grep -IR '^[^#]' /etc/polkit-1

cat /usr/share/polkit-1/actions/org.debian.apt.policy

EDIT: After you've uploaded the files I can see that the problem is in your /var/lib/polkit-1/localauthority/50-local.d/20-xbmclive.pkla file which seems to have been installed by XBMC and effectively turns off all authentication via polkit (why it has done so and if it is really needed I don't know, I don't use this software).

[XBMC-Live user permissions]
Identity=unix-user:azizjoh
Action=*
ResultAny=no
ResultInactive=no
ResultActive=yes

It's improper to say that: "It seems that on Ubuntu, calls to sudo from the GUI are somehow being intercepted by pkexec". pkexec doesn't have much in common with sudo. In contrast with sudo, pkexec does not grant root permission to an entire process, but rather allows a finer level of control of centralized system policy.

Now, if you want to run a GUI application without being asked by a password by pkexec, this is not difficult to be done. Let's take for example GParted. When you open it, you will see the following dialog window asking you by a password:

Click Details and the dialog window will look now like:

From here all you have to do is to open /usr/share/polkit-1/actions/com.ubuntu.pkexec.gparted.policy file using for example the following command:

gksu gedit /usr/share/polkit-1/actions/com.ubuntu.pkexec.gparted.policy

and change the following lines:

      <allow_any>auth_admin</allow_any>
      <allow_inactive>auth_admin</allow_inactive>
      <allow_active>auth_admin</allow_active>

with the followings:

      <allow_any>yes</allow_any>
      <allow_inactive>yes</allow_inactive>
      <allow_active>yes</allow_active>

Save the file and close it. Next, when you will open GParted you will not be asked for a password anymore.