I had the same problem: several Applications preinstalled on my MacBook were somehow assigned to other person's Apple ID. I didn't even have to buy new copy, everything was solved by simply contacting App Store Support.
I wrote an inquiry in this section: https://expresslane.apple.com/Issues.action, Apps and Software -> Mac Apps -> Mac App Store -> Purchases, Billing and Redemption -> Other topic — it suggests to contact them via email, doesn't require any support account (my phone support and others have expired long ago).
In my request I just described the situation and they assigned a new iLife pack to my Apple ID for free, without asking for any documents, only macbook serial number. I just needed to follow their instructions: remove applications, some files and then install new copies from App Store. This process didn't affect any libraries, all my photos are safe and sound.
Hope, it'll work for you too!