I have the same problem but have figured out the following, which I hope helps someways to figure out how to fix these problems.
If you open iTunes and look under Store, View Account - it shows a true Apple ID (with Email). Click this and you get an Account Summary. Look down further to iTunes in the Cloud, Manage Devices. Click this and you will see Associated Devices (iPad, iPod etc) 'managed' by the Apple ID (email) seen earlier. It is THIS Apple ID that has Adminstrator Privileges on the device(s) and so why, on the device in question, you get the 'You are not a member of the administrator group' message when you are not signed in using that Apple ID on the device, eg. using a Nickname only ID in Games Centre.
There are tick boxes you can uncheck to remove the devices from the control of the Apple ID shown in iTunes.
But, before you do..
An 'Apple' ID that just has a Nickname (no email) can never have Adminstrative rights as it is a Childs Account (when the Birthdate is entered as <13). These 'Nickname' IDs can only be created in the Games Centre App on the device - it is misleading to call it an Apple ID really. It is the only way you can create a GC account to play without inputting any personal or Creditcard details in. However, the main Apple ID (with email) has to have been logged in on the device at some time beforehand and downloaded the Apps - the device remembers it. This main Apple ID account then automatically 'manages' the Child account from there on. When logged in under the 'Nickname' account, no Apps can be downloaded or In-App purchases made. If you try and do so, you will be prompted for the 'Managing' Apple ID (& email)'s password. It's a safeguard to prevent kids buying out the store or having your Creditcard details on numerous ID's/devices. Likewise, you can't log in via Apple Stores or sites with this Nickname ID as it isn't a valid Apple ID proper. No creditcard, No full account basically! That's why a Nickname ID can never be updated or changed. There isn't any way to security check and validate the account.
This part I am not sure on..backup devices before doing anything!
However, if you create another proper Apple ID (& email) via iTunes or App Store, meaning an Adult Birthdate and supply Creditcard details etc. on the device, then log out of that and via the Games Centre App, log in as the Nickname Account, I think this will then link to that Apple ID, rather than the previous one - freeing the previous 'owner'. As before though, you will have to log into the new Apple ID&email account and use the password for any purchases.This way, you can log in and keep your progress on any GC games played under the Nickname. If you don't care and want to start afresh, just start a new GC account/game using the new proper Apple ID on the device.
Just one more thing though, any Apps already on the device will always be owned by that original Apple ID. If you want ownership, you will have to delete the App(s) and download fresh under the New Apple ID (email). The Nickname can never own anything.
My brain hurts...