I can see that you could potentially form a similar explanation around that scenario too but it doesn't seem as convincing.
In most places, crossings work on a parallel/perpendicular system: parallel roads and pedestrian crossings are red or green[1] at the same time. This means that cars turning across a pedestrian crossing must give way (yield) to pedestrians.
The UK system, by contrast, isolates the pedestrian phase from traffic phases: when the green man (the WALK indicator) is displayed, no vehicles will approach the pedestrian crossing from any direction. The time between pedestrian crossing opportunities is longer, but there is no contention for the crossing from cars turning into the road.
The article describes the parallel/perpendicular system. In this scenario, a driver will see a parallel WALK light and a (vehicular) green light at the same time. As the pedestrian crossing typically goes red earlier (because people take longer to cross the road than cars take to cross the intersection), a car driver who watches the pedestrian crossing light or countdown timer gains advanced knowledge of the parallel traffic signal.
1. Or white in some places in the US!
There is also a distinction between green and green arrow turns. Green arrow indicates safe turns and green means yield to traffic/pedestrians.
It is likely that once the cross walk reaches zero, a yellow light will appear on the traffic signal. Anyone reading the walk signal in front of them will have an early warning about the traffic light and may try to speed up to get through.
If you're a block away from the light and you see a "4", what do you do?
The most "famous" example in Europe of all traffic being stopped at once, I suspect is Oxford Circus in London, where they changed to start doing this a few years ago.
The reason to do it there, though, was to allow pedestrians to walk in any direction (diagonally as well) across one of the busiest crossings in the country. This BBC article refers to it as a "Japanese-styled system":
There are also plenty of junctions where some car drivers are allowed to proceed while on other bits of the road, pedestrians are allowed to cross. So (typically) each road into the junction has a central island and the pedestrian controls for each half of the road are separate. On those junctions, it's never safe to go across the middle as there will always be some traffic moving.
There are two okay solutions - either you desync the lights, so that there's some gap where the pedestrians have a red light but cars already/still have green, so that they can make that turn; or you make a 3-phase crossing; A-cars have green in one direction; B-cars have green in the other direction; C-all cars stop and pedestrians can cross across and diagonally. It works okay.
What's not a solution - 'right turn on red' doesn't solve it; this problem matters in heavy car/foot traffic, and in such traffic there aren't any safe opportunities to do so.
In the UK/Europe, green means go and red means stop, without the above exceptions. In order to make this work, pedestrian crossings are often segmented, with individual signals for each section. There are a few junctions where all traffic is stopped for pedestrians, but that is pretty rare. Most junctions just allow pedestrians to cross on sections where traffic is not travelling.
UK/Europe also has a lot fewer crossroads than US. Since the cities are older, and do not as often have a grid structure, there are a lot more three-way junctions than crossroads, which actually makes crossing the road easier.
[0]: http://ntl.bts.gov/lib/25000/25600/25603/DOT-HS-806-182.pdf
This varies by location. For example: In NYS it's allowed unless banned by a sign, but in NYC it's banned unless allowed by a sign.
But yeah. I had trouble understanding the issue at all, as you note London has them, I've never noticed any issue at all - if anything, it gets the peds out of the road more timely...
In the US, the walk lights go 'green' at the same time as traffic parallel to the crosswalk gets a green light, in a shared phase. So if the timer is getting close to zero, it means the vehicles are about to go to a red light, and the opposite direction is about to get the green light.
In fact, here's a discussion in the UK Parliament in 2004 where it was proposed to restrict the use of all-red phases in low traffic junctions, and where the person proposing the change saw it as necessary to describe why this was even an issue:
http://www.publications.parliament.uk/pa/cm200304/cmstand/a/...
"Mr. Redwood: Until a few years ago, no one would have understood why new clause 5 would be necessary. All traffic lights that motorists or cyclists encountered on our highways had a simple form of operation which meant that there was always one free route across the junction showing green. In the normal four-way junction where two roads intersected, one road had priority for one phase and the other road had the alternate priority. There could be more complicated variations at larger junctions, but there was always a green phase for vehicles on one part of the junction"
[The proposed clause 5: 'No authority shall be entitled to install or operate traffic signals with all red phases at road junctions where there is no hazard other than traffic.']
You may be right that no vehicles will have green light to cross the pedestrian crossing while pedestrians have a green light, though I'm not 100% sure that's true either - I seem to remember crossings in London at least where turning traffic will have green at the same time as pedestrians, but I don't drive so maybe that's just me as an impatient pedestrian misremembering, as I'll regularly cross on red.
All-red phases are a slightly different issue, and indeed, not all crossings have them
I was describing the crossroads situation where all vehicles are allowed to travel in any direction when they have a green light (no filter light/lanes), as this is the most commonly occurring situation in towns in the US I think. Not including states where there is a propensity for 'no left turn' intersections.
In the US, this would mean two phases, with each one being a shared pedestrian and vehicle phase, pedestrians crossing in parallel to traffic. In the UK this would be three phases, two traffic and one dedicated pedestrian phase.
I personally prefer the UK system, as in the US as a pedestrian you are at the whim of drivers paying attention to pedestrian traffic, and even if they don't hit you they may well start turning the corner to pressure you to hurry up.
The issue is that vehicles moving in the same direction as the pedestrians can also see the pedestrian countdown and can use that information to determine approximately how much longer their own vehicle light will remain green.
The article suggests that that different drivers interpret the countdown information differently than the green/yellow/red lights and more specifically, and unlike the colored lights, different drivers interpret the countdown timer differently (some see 3 seconds and speed up, others see 3 seconds and slow down).
To address your question, which I (humorously) don't really get -- the pedestrians who have the countdown and the cars are moving parallel to each other. The drivers and the peds are both looking in the same direction at the countdown timer.