Q: Trying to install a fresh copy of OS X 10.8

You and your family member will run into continuing problems until you follow these instructions. There is no way to transfer Mountain Lion's license, but Mavericks is free.

Since it will stay in the family securely erasing it is probably optional, but that's for you to decide.

What to do before selling or giving away your Mac

In addition to the above:

• If you enabled FileVault, disable it in System Preferences > Security & Privacy.
• "Deauthorize" your iTunes account. Same for Audible if you have one.
• System Preferences > iCloud > de-select "Back to My Mac" and "Find my Mac".
• Sign out of iCloud. Select "Delete from Mac" when it appears.

Then:

• Start your Mac with its original System Installation DVD (if your Mac shipped with one) or OS X Recovery (if it didn’t).
• Remove any Open Firmware password if you created one: select Firmware Password Utility from the Utilities menu and remove it.
• Select Disk Utility from the Utilities menu.
• Remove any partitions you may have created.
• Select the Mac's hard disk icon, then select the "Erase" tab.
• Select the "Security Options" button and erase the disk.

The more "securely" you erase the disk, the longer it will take. The fastest method is sufficient since all but the most expensive techniques and equipment will be able to recover securely erased data.

• When it finishes, quit Disk Utility.
• Select Install Mac OS X from the Utilities menu. Do not create any user accounts.
• When it finishes, shut down the computer.
• If you want to install the bundled apps that were included with your Mac, restart by using your Applications DVD and install the bundled apps.
• Don't forget to include any DVDs that came with your iMac, your AppleCare certificate if you bought it, printed documentation, even the box if you still have it.
• Execute a bill of sale showing the Mac's serial number.
• Once no longer in your possesion, remove the Mac from your devices in My Support Profile.

Which OS version did this computer come with originally?

If you were using the original install disk, you wouldn't need an Apple ID. You appear to be trying to use recovery. It looks like the Mac came with an OS earlier than Mountain Lion - in that case, you cannot give the Mac away with Mountain Lion on it as that license is not transferable. You have to sell/give away the Mac with the original OS version re-installed. It won't work any other way.

This is what you need to do:

John Galt wrote:

 

...

• Start your Mac with its original System Installation DVD (if your Mac shipped with one) or OS X Recovery (if it didn’t).

Every MacBook shipped with a DVD. Use that. No Apple ID will be required.

As babowa wrote, you can only transfer ownership of a Mac's originally installed OS. In your case that was either OS X 10.5.x "Leopard" or OS X 10.6.x "Snow Leopard".

If it was the former and you do not already have a Snow Leopard upgrade DVD, you will need to purchase one before you can upgrade that MacBook to Mavericks:

Online (US): http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard

You cannot reinstall Mountain Lion without the Apple ID used to purchase it, but that is of little consequence since Mavericks can be installed and will run better on any MacBook that can run Mountain Lion, and it's free. So, the most you will have to spend is $19.99 US and that's only if you need to purchase Snow Leopard.

I realize that this purchase is not for a download but for a DVD that will be mailed.

That's not the case - what you're purchasing is a download code that is "redeemed" in the App Store to purchase Mountain Lion:

"What do you receive: An email with a content code for the Mac App Store."

Read the link you posted. Snow Leopard is a prerequisite - see what it says under "Your Mac needs" following "System Requirements" at the end of the page.

To transfer ownership you need to follow the instructions I posted. That's the only way to avoid the problems you're encountering.

If you no longer have the MacBook's original System Install DVD you can contact Apple and purchase a replacement. The fee is reasonable - about $25 including shipping.

Apple will need the MacBook's serial number: MacBook: How to find the serial number

Follow what I wrote and you'll be all set.

To second John Galt's suggestion:

No, what you want to do will not work.

It makes no difference whether you are selling it to a stranger or giving it to someone - you still need to follow the licensing agreements or there will be nothing but problems. If you do not wipe the drive and  reinstall the original OS, then the recipient cannot re-download/reinstall/update - ever.

You need to get the original install media, wipe the drive, reinstall it, and then the recipient can download Mountain Lion or Mavericks with their own Apple ID.

Unfortunately, if you upgraded to Mavericks using your Apple ID, it will leave the recipient unable to reinstall, etc. The license is not transferable, so the recipient will need access to your Apple ID and password in order to do any updates, reinstalls, etc. It is not a good idea and violates the SLA.

Great! Thanks for the update, and don't lose that DVD.

Glad to hear that so there won't be any problems down the road for him/her.