There are three MAJOR things that the study doesn't mention:
1) Of the people that downloaded the album (let's make up the number 4 million, just for sake), how many of those people would've bought the album in stores anyway (or the "regular" way)? Right there, what if the answer was 1 million? So... 1 million people would've been willing to pay $15 for it in stores. Instead (still just making up numbers), 750,000 paid, say, $15 for it. 750,000 paid, say, $5 for it. Then you have the remaining 2.5 million people that just got it for free (who would've otherwise picked it up in a record store, flipped it over, decided against it, and put it back on the shelf and not purchased it anyway).
2) How much money is Radiohead making off of this venture, per transaction, versus how much did they make before? If Sam Goody's sold a $15 Radiohead CD in 2002, how much money did Radiohead see from it? Maybe $3? $5? I have no idea. But I know who was getting the biggest piece of the pie. The record industry (duh). Now, if someone went to their site and paid $8 for it, how much does Radiohead get? Well, $8. Minus their expenses for running the site, etc.
So... take 750,000 paying $15 and 750,000 paying $5... that's $15 million. The other way - 1 million people paying $15 in stores - would be the same thing: $15 million. Is Radiohead making more off of the $15M give to Sam Goody's, or the $15M coming directly to them? That's a no brainer. They make more money when they cut out the middle men... the CD manufacturers, the distributors, the industry executives, etc.
3) I've been making these numbers up, so they're obviously inaccurate. Let's say I'm way off, like Radiohead only pulled in $1.5M from their site (from which they'll subtract expenses) when they could've gotten $15M through the regular channels and then received, say, 50% of that. If my numbers are that far off, then it means that they made only,say, $350,000 total, instead of $7.5M from the industry. The AP "study" might interpret this as a loss of $7.15M. The loss will probably be covered, and exceeded, from those 2.5 million people that downloaded their music for free - the same people that would've otherwise not purchased the CD from the store. Their new download-for-free fans will generate new revenue for them. Of those 2.5 million, let's say they get 250,000 new big fans. Of those 250,000 new big fans, let's say half of them pay $65 to go to the next Radiohead concert, and half of them purchase the new $82 box set that's coming out. Do the math on that, and it's an additional $18,375,000 in revenue that would've never existed without the availability of the free downloads. That $18.375 million well makes up for the delta in the album sales loss by switching to their proprietary model.
Point being, the gain of new fans will exceed the loss in sales - and that's only assuming that they did lose out on money. It's possible that they made more money on the front end anyway, and - in addition - will continue to make more money on the back end from their new fans.