RLJ (Red Light Jumping). (The definitive bikeradar thread)

Had this not been at a crossing there'd have still been a duty of care on the driver (and case to answer possibly), however the presence of the crossing made the driver automatically in the wrong for the collision with the pedestrian - which is why they argued it was a rider not ped, and why the judge used those specific words.

Note that Crank vs Brooks was the appeal case. In the original case the defendant (car driver) was found to have no case to answer (even though it occurred on a crossing).

I might be wrong, but thought the significance of that case is that pushing =/= riding.

Yes, but people read too much into it, specifically that pushing a bike is the same as walking without a bicycle. It's not, it (pushing a bike) was just adjudged not to have any relevance when using a pedestrian crossing by foot. It (pushing a bike) may still have relevance when pushing it across a junction.