For fans of Taylor Swift, this seemed like a great story of David vs. Goliath—or perhaps pop Goliath vs. even larger consumer-electronics Goliath, depending on how you look at it. And standing up for independent artists and winning what appeared to be a historic reversal from a company like Apple is definitely worth celebrating. Swift is clearly not just a pop singer, but a smart businesswoman who thinks about these kinds of issues and is willing to speak up about them.

From a straightforward PR perspective, or even a bottom-line financial point of view, Apple changing its mind isn’t that surprising at all: Not paying artists makes the company look bad in front of other musicians and their fans, and altering strategy at this point is going to cost a tiny amount of money—essentially a rounding error for a company its size.

But as my colleague Philip Elmer-DeWitt has pointed out, this tale is partly about how the balance of power in the music industry has shifted, and how that gives individual artists like Swift a lot more pull than they used to have. Apple may have a market value of $700 billion, but without the content from top-selling artists like Swift—and the marketing support that comes from her millions of devoted fans—the company’s fancy new music service wouldn’t be worth much.

It’s not just about Swift though. Apple is also trying to manage the transition from the existing pay-to-download business (which it pioneered) to the new streaming model, and to some extent it is playing catch-up with companies like Spotify. So it needs the support of artists and labels even more than it would otherwise. As one music-industry insider told me recently, Apple can no longer count on its dominance in the recorded music business to dictate terms to the record labels. They now have Spotify and others to play ball with as well.

“Apple wants to kill free because then it can win vs. Spotify,” this source said. “But the labels don’t want to be back in a place where they are beholden to Apple and they get dictated to — they want three or four strong players so they can play them off against each other.”

Apple would very much like the labels to go all-in with its service and cut out Spotify, and it’s trying hard to convince them that they should do so—in part by appealing to their dislike of Spotify’s permanently free tier (something Taylor Swift has also come out against in the past, arguing that it permanently devalues music). Still, the labels know that free is probably always going to be an option. In fact, many of them like having free because it is a low-cost marketing tool, the way radio used to be. Not to mention they are happy to have at least one strong competitor to curtail Apple’s power as well.

There’s an even larger, long-term picture that gives the record labels nightmares, and that’s the prospect of Apple cutting them out of the picture altogether—in other words, going to individual artists like Taylor Swift and striking a deal with them directly, to market them and distribute their music. “Ultimately, they know Apple wants to go directly to artists and cut deals with them,” said the senior music-industry executive. “The labels aren’t the fastest moving but they are not dumb. So they need something to blunt Apple’s power.”

There’s no question that Apple would have a compelling offer to make, assuming its music service achieves anything like the kind of market penetration it is hoping for. Partnering with the company would put an artist’s music on hundreds of millions of devices around the world instantly, and with its financial strength it could afford to cut some very favorable deals. It’s definitely in Apple’s long-term interests to stay as friendly as possible with million-selling pop artists.

In the meantime, back-tracking on its no-fee plan makes Apple look a little more humble than it typically does. And it won’t cost the company much at all. Still, the back-and-forth with Swift is much more than just “theater,” as Pandora co-founder Tom Conrad argued on Twitter. There are tectonic financial shifts underway in the music business, and Apple is planning to play a big role in where those continents wind up when they finally come to a stop. Making nice with artists like Swift is just part of that larger plan.

Follow Mathew Ingram on Twitter at @mathewi. You can read his coverage of the digital media industry here or you can subscribe via his RSS feed.