Bebung is a specialty of the clavichord, where it's possible to make a sort of vibrato after the key is already pressed.
On a normal piano, Bebung is impossible. Perhaps Arrau used the word in a wrong context.
https://en.wikipedia.org/wiki/Clavichord
Bebung was the name of the original technique for vibrating the string on a clavichord, but the
effect is not the same as the technique; after all, Beethoven composed the effect into his sonata op.110 in A-flat major. It isn't possible to add vibrations to the string on the piano, obviously, but it is possible to imitate that sound. Arrau's technique is the correct one, and is also the technique one would use in Classical music for forte-piano dynamics (for instance the last movement of Schubert D960, or the second movement of Beethoven op.10 no.3).
I don't know the physical reason for it, but playing like this takes most of the body away from the sound, leaving a sort of echo, which if you were imitating Bebung, would sound like a vibration of the note, rather than two notes (this is the technique employed in op.110).
A similar technique, used a lot by pianists of the old school but hardly at all these days, is playing
staccatissimo chords, and grabbing their vibration with the pedal the split-second after you release the keys.
Walter Ramsey