Not completely understanding what you mean by "psychology" of practicing, I'll now just make a banal note that in my case, 95% of practicing takes place off the piano. Away from the keyboard I tap the table, I concentrate on how to specifically activate the nerves without increasing tension in parts where it is not necessary, I visualize the keys, sometimes I try to transponate a passage... I would interpret that by "psychology" you meant things like attitude, motivation et cetera, but if you were wondering about the whole mental side of it, then of course it is important as your brain is also where the physical execution ultimately takes place.
Although I haven't seen the show, I would guess that somehow Derren made her "play the piano in her mind". The piano itself is just a physical object, its your brain that has to form a solid mental structure of all the relations between keys and scales and adjust your physical capabilities and limitations to those relations. I've myself had an instance where I taught myself the physical execution of a certain passage in a dream, and when I did wake up I found out that I could play through it flawlessly (as flawlessly as it was possible for me with that horrible fingering). I like to think practicing is a lot like tinkering; You figure out the essentials and the unnecessary yet natural habits/tendencies, then you take the essentials, drop everything else, and figure out ways to arrange that material (for example a certain technique beyond your current motoric ability) so that it "clicks" with the medium (being the instrument).
And there I said probably nothing of much substance, but you'll have to excuse me for I am tired and this subject would always get me carried away!