And yet, any professional musician will claim that practice is an essential part of the craft, required for learning difficult sections and tightening up loose licks. I wonder why these two viewpoints come to such opposite conclusions.
It absolutely is. Practice is necessary but not sufficient for high-level musical performance. The study talks about musical ability in terms of rhythm, melody, and pitch discrimination -- mental skills around music -- and finds that these are not changed with practice. These two statements are not in conflict.
Exactly. I think the paper is trying to establish that there is some kind of inborn talent that is not affected by practice, even if other things (like performing ability) are.