Some masters are guarded jealously by their owners. For example, I've heard that some of the Stevie Wonder releases aren't even from the masters, because he won't part with them. Some masters may truly capture something irreproducible; say, John Lennon's hoarse voice in "Twist and Shout."
In this particular case, at least, Taylor Swift has put the lie to the uniqueness of the masters. If she has the right to rerecord everything, the old masters aren't so special. But I think the article is also right. After this exercise, she may have made her point, and may force Shamrock Capital to make a deal.