I heard Alicia De Larocha play this live and was awestruck. I met her afterwards, and my small hand engulfed hers when I shook it. 
How does she do it?
She does indeed have small hands.  Tiny.  As to how she does it?  She just does.  I've met her a few times, and she's always been very gracious and humble, unassuming.  And she actually helped a friend of mine who was having problems with pre-, during and post-performance nerves.  My friend asked her if she had ever had a problem with nerves, she responded with a resounding, "
Si!".  After a bit more chat, she suggested to my friend that she take a Vitamin B supplement since that's what helped her.  And, lo and behold, that did the trick.  *And my friend even went to her doctor just to make sure it was the Vitamin B helping her deal with her nerves and not some power of suggestion... Sure enough, after some tests, her doctor found that her system processed Vitamin B very fast, so, in essence, she was Vitamin B-deficient for most of her post-adolescence life.  Not anymore.  (Since Vitamin B is an important component of proper nervous system function...)
In any case...
Ms. de Larrocha is indeed an amazing pianist, although, I believe she recently retired from concert life.  I seem to remember a "farewell tour" in the recent past for her.  Thankfully, her recordings of the major works of the Spanish canon - Albeniz, Granados, de Falla, etc. - have remained in circulation over the years.