I would do that. I had this issue whith someone else in your exact position. They had a Dell CD and a legitimate product key and wanted to install it on another machine. Just reassure the rep 9in a nice way) that this key is only being used on one machine, and you won't have any issues.
And I don't see anythign illeagal about borrowing an install CD from someone when you have a legit product key, especially with something such as XP that has a key system that actually works.