A motionless photon?

I just read a new science article that jarred my sense of reality: http://www.sciencenews.org/view/generic/id/330958/title/Wave_function_directly_measured_ where an experiment "eliminates all photons that were moving, leaving only the photons that were still."

Reading that image, of a photon being still, motionless, really got to me. Retracing my mental steps, I realized that my concept of a photon implicitly required it to be moving, and moving at the speed of light in the medium within which it is traveling at the time. How could it be motionless?

I suppose that a photon could be perceived as motionless by an object moving in parallel path alongside it also at the speed of light. Which seems to mean only seen as motionless by another photon. Maybe then measuring the parallel photon one could determine what it "saw" of the first photon. But this leads into foggy thinking land. Not likely.

I then realized that my concept of a photon was that it was a thing that has its motion at the velocity of light, as part of what it is. It is an ever-swapping exchange of electric and magnetic fields ever going in some direction and it happens at the speed of light; being light, of course. Velocity is part of what it is. Presumably the vectors of the electric and magnetic fields define its direction and velocity. All a package.

And since electric fields and magnetic fields are things that exist spread out beyond the point of concentration, so also the individual photon is spread out; the wave function thing. As the photon tools along swapping its energy back and forth between electrostatic and electromagnetic fields, the rate of swapping back and forth defines its energy content but not its speed.

A motionless photon? The very idea just warranted a blog post to help soothe my sense of the rightness of the Universe, or something like that.