Well it has been a month or so since I did a install of OS X so I'm not completely sure if you can proceed to the next page without entering a password.
So I suspect you did enter a password. For your future infomation when you are preping a system for Resale you must reinstall the original version of OS X that came on the system when it was new. If at one time you had upgraded the Mac you sold to any of the Download only versions of OS X that version is TIED to YOUR Apple ID not to the system. That is why it is very important to reinstall the Original shipping version of OS X.
What is happening now it the new owner is trying to Update that system and it is looking for YOUR Apple ID and the password for it.
The only thing the new owner can do is use the Online Internet Recovery system, which is what you should of used instead of the Recovery HD partition on the internal drive, to reinstall the original version of OS X that came on it. That is IF it originally came with Lion or Mt Lion Pre-installed.
IF it originally came with DVD system reinstall disc I do hope you supplied them with the system when you sent, gave, that system to the new owner. Because if it came with any version of OS X prior to Lion coming out the new owner will need to reinstall OS X and the iLife apps from those original system discs. As all other verison of OS X you installed are Tied to Your Apple ID and can not be transferred to another person.
So answer these questions.
1) What version of OS X came on the system when it was brand new?
2) If it came with a version of OS X prior to Lion coming out, June of 2011, do you have those original system discs?
3) If two is correct did you send those disc to the new owner?
You do realise that if you had provided all that info in your original post we might have this all figured out by now.