How to avoid associating your Apple ID with your Mac’s account in Mountain Lion
One issue that’s come up in the wake of Mat Honan’s troubles has been how Apple has built easy ways to associate your Apple ID with your account on your Mac. One of those associations is an option to use your Apple ID’s credentials to reset your account password on your Mac.
I personally don’t want to have my Apple ID associated with my account on my Macs (especially since I can still set up all the iCloudiness I want using iTunes and the iCloud preference pane), so I don’t set that up. See below the jump for how to avoid associating your Mac’s account with your Apple ID and also how to remove an existing Apple ID from your account entry in System Preference’s Users & Groups preference pane.
How to skip Apple ID setup on login
When you first upgrade to Mountain Lion, or when you’re setting up a new account on a Mountain Lion Mac, you’ll be prompted at login to enter your Apple ID.

To avoid entering your Apple ID at this point, click the Skip button in the lower-right corner.

Click the Skip button at the next window to confirm that you want to skip signing in with your Apple ID.

Click the button above Start Using Your Mac. After that, login will complete and your desktop will come up.

Removing your Apple ID from your account in Users & Groups
If you had previously associated your Apple ID with your account, here’s how to remove your Apple ID from your account on your Mac.
1. Open System Preferences and go to Users & Groups

2. Select your account.

3. In the Apple ID: section, click on the Change… button.

4. In the drop-down window that appears, select your Apple ID account.

5. Click the minus (-) button in the lower-left corner of the window. Your Apple ID should be removed.

6. Click the Done button.
7. In the Apple ID: section, the Change… button should now be a Set… button. Your Apple ID should not be listed.

Now, your Apple ID should no longer be associated with your account. That will remove the ability to use your Apple ID to reset your password.
Or you could just uncheck the checkbox that says “Allow user to reset password using Apple ID”.
Sorry. You did show that in the first screen shot. If you’ve disabled password reset by Apple ID, why disassociate the account? What other powers does it have?
I have found that disassociating the apple id from a user account also disables the ability to connect two computers using the ID rather than username and password. I kept having problems with the latter not having the same user rights to some of the files on the remote computer.
I wonder if anyone knows if removing the Apple ID completely from being associated with the user causes any unforeseen side-effects? iCloud doesn’t seem to use it in its System panel, and continues to show the original ID it after I turned it off in the Users panel.
Just seems I can sign in with an Apple ID in too many places: User panel; iCloud panel; Mail prefs; iTunes sign in; iTunes Home sharing; FaceTime; iCal;
Yes, it has become a mess. It would be more convenient to sign in once and then turn individual services on and off as needed.
I think here it is used for identification while connecting two mac’s rather than the usual id and password.
that option seems to be gone now. appleID