After reading your open letter to Apple, I couldn't help but feel for the musicians who will not be paid for streams played during the three month trial period of Apple Music. I am not a professional musician, and I do not understand all the complexities of the music business. However, I do understand copyright law in the Unites States, which grants the creators of a work the right to control the distribution of that work. Since Apple music is not eligible for a statutory license like a radio station is, the only way Apple has a legal right to stream your music, or any other artist's music, is if they negotiate for and purchase that right. And the only way Apple could do so without negotiating with you is if you already sold that right to someone else, like your record label. So Miss Swift, if you don't like the deal your record label's distributor negotiated with Apple, perhaps you should not have sold the copyright to your songs to that label for them to do with as they please.
Where is your open letter to Big Machine Records (your label), and Universal Music Group (your label's distributor) who actually sold the music to Apple? I guess you weren't thinking about this when you were 15 years old and some producer or label executive discovered you and offered you a recording contract. You probably got paid some money, and got some studio time, and got a great producer, and everything was amazing. But you also gave up your copyright to the recordings.
So the artist in me feels for you and other artists associated with the big labels and distributors who will have to give away three months of free streaming. But the businessman in me feels like you are getting exactly what you signed up for.