|You are correct in all your assumptions. It's very likely that one of two things happened:|
1) your friend installed XP using a CD key other than the one on the bottom of the laptop
2) your friend installed XP using the key on the laptop, but it has also been used to install XP on other computers
You should try to find what key was used to install XP on your laptop. If it was not the key printed on the sticker, then you should change the key to the one on the sticker.
this will help with all that: http://pcsupport.about.com/od/tipstricks/ht/findxpkey.htm