To paraphrase drastically: the RIAA says that sales are down 10% because of piracy and Soundscan (the Neilson ratings of music sales) says sales are up nearly 10%. They are both right, sort of. RIAA counts a "sale" as a unit shipped to a store, Soundscan counts a "sale" as a comsumer buying a unit from the store.
To borrow the author's great simple example: If I own a record store and Q4 2003 I ordered 1000 Brittany Spears CDs and I sold 700 of them. Then in Q1 2004, I sold 770 CDs but I only ordered 930 from the supplier. Q1 vs. Q4 shows an increase from 700 to 770 units that I sold to customers, but according to the way the RIAA measures things, my "sales" would be down to 930 from 1000.
Why is this? The author did ask this question, which was neatly evaded by the RIAA spokesperson. Basically, I think it's because the RIAA wants to say that sales are down because of piracy and filesharing, thus justifying it's protection-racket of sending people letters that basically say "send us money and we won't sue you". See, that Econ you took in college does come in handy!