Yesterday marked the first time ever that Apple approved an on-demand music-streaming program for the iPhone. Rhapsody just so happens to be the lucky star.

When Rhapsody submitted the app to the App Store for approval two weeks ago, the media and blogosphere questioned endlessly the chances of approval vs. rejection, with good points made on either side. Though apps that emulate radio functionality, like Pandora and Last.fm, have been available through the App Store for some time now, approving Rhapsody would be a big step for Apple because it is direct competition.

With the Rhapsody app approved, users can now opt out of purchasing iTunes Store music and, for $14.99/month, they will now be able to stream the entire Rhapsody library through their iPhone.

So where did this approval of such stark competition come from?

Maybe it’s a result of yesterday’s boost of confidence that came with Apple’s reminder to everyone that, with 8.5 billion downloads to date, the iTunes Store is undeniably the #1 music retailer in the world.

Here’s what’s more likely: facing close scrutiny recently from the Federal Communications Commission (FCC) over its repeatedly strategic rejection of apps that compete with its own services, Apple may be letting this one slide to prove to everybody that they aren’t as anti-competitive as they might have appeared to be.

Could this spell the beginning of the end of Apple’s massively dominant music sales? Not immediately, at least.

While Rhapsody will certainly be providing a convenient service for many of its customers (and new ones drawn from the Apple crowd), it has its drawbacks. Though the service boasts a library 8 million songs strong, they will stream to user’s iPhones at 64 kilobits per second, a considerably lower quality bitrate than the 256 kbps songs available for purchase on the iTunes Store. Also, good luck listening to music through Rhapsody when service is unavailable, like when you duck down into a subway.

In the end, Rhapsody will still be for people who need to hear just that right song at just the right time and the regular iPod functionality of the phone will be sustained for fans of higher-quality tunes and consistent tunes, at that.