[jfengel]

Not necessarily. They imagine a kind of shutter that could close in the middle of a photon's wave.

That's not quite as ridiculous as it sounds: a microwave photon could be centimeters long, and a lower-wavelength photon could be meters or more. You could think of the shutter as an LCD screen, which could change from clear to dark in less than the time it would take for a meters-long photon to pass through it.

You can't actually do it, though the speed of light isn't the reason. The calculation is for an infinitely thin, infinitely black barrier. You could do an approximation of it, but the complexity of the approximation swamps the already-complex wave form the theory gives.