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
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).
Bebung can be done on a piano, although it doesn't work well for a vibrato effect. It's used to imitate older pianos, on which the sound would decay much faster. Anyways, the idea of the technique is to lightly tap the strings with the dampers so that the sound decays faster, that way you can do a fortepiano on a single note. This is used with some frequency in the grave part of the first movement of the pathetique for example. This can also be done with the damper pedal, the idea again being to let the dampers down just enough to let the fuzz contact the strings without completely dampening the sound.
A pianist of today that uses this fortepiano effect a lot is Olli Mustonen. Listen for instance to his Pictures at an exhibition, "The castle", where he does it in the sforzando chords - there are numeous instances where he does it throughout the piece but I don't remember them. In "the catacombs", where you have sforzando chords and then a piano (or pianissimo?) chord with some notes from the sforzando chord tied over, he plays sforzando only on the notes that are not tied over to the next chord - probably the best solution.