(The fact is, according to the BBC, they are sometimes right. In New York, they are sometimes referred to as "placebo buttons", and in the UK, well - it depends. If you are at a standalone pedestrian crossing, unconnected to a junction, the button will turn a traffic light red. At some crossings, the button will work, but only between the hours of midnight and 7 a.m. In the daytime, the button has no effect.
To be honest, I don't care, I'll still keep poking them.)