Using Your Reward Checks

I already mentioned that Office Depot will have more free after rewards deals tomorrow, but I was thinking about these deals today.  No matter which way you look at it, you end up with extra spending power at the store where you earn the rewards but what's really "free" in the deal?  Is the original purchase that you get the reward from the free item or is it the item you buy with your reward check?

A few months ago, I bought moving boxes when they had a 100% back deal.  I was getting ready to move so the sale really was perfect timing.  Today, I used my reward check from that purchase to buy a desk and chair for the second bedroom of my new place.  Not only did the reward check cover the entire purchase, I still have a balance on my reward check.  So which was really free?  The boxes, which I needed anyway, or the desk, which I planned to purchase once I finished unpacking the new place?  Or should I consider them each half price since I would have purchased both regardless?