Makes Perfect sense if you accept this was a PR stunt planned by Swift's management and Apple from the very beginning.
Look at the facts
1. This 'situation' allows Taylor Swift to come out as supporting streaming services as the 'savior' of small artists, without looking hypocritical for reversing her decision and views on Spotify.
2. Apple gain a huge amount of positive PR by creating a massive trending discussion and global news story featuring two extremely powerful brands (Swift and Apple), just before the launch of their new service.
3. Apply have spent months if not years working the financials of the streaming deals - but suddenly overnight they re-work all the numbers to make it work in favor of the artists? No chance, this was planned for a long time.
After the fact, a 'conspiracy' many times looks legitimate.
But imagine Taylor Swift and Apple getting together in secret meetings to discuss this. How do they know how public reaction will go? Maybe Taylor Swift is hurt because people think she's whiny? Maybe Apple is hurt because people think Apple is money-grubbing? And won't accept Apple's about-face? Planning something and an actual outcome matching what you want won't work most of the time.
The most likely thing that happened is that Apple was using standard industry contractual agreements, didn't know it would ever get out to be publicly known, when it did, Apple didn't like the bad press, calculated what it would cost to 'save face', saw that they could afford it (and it was worth paying vs. bad press), so did an about-face.
I agree with Taylor Swift on this one, and I'm ashamed of Apple's initial position, and glad they changed their minds.