I assume they are using the theory/algorithm from the MIT video magnification work: http://people.csail.mit.edu/mrub/vidmag/

For this purpose, MIT's Eulerian Video Magnification is next to impossible when you have both color changes and large motions (it is better suited to magnifying small motions, or subtle color changes in unmoving patches). NASA Glenn's thearn has developed another approach which has the same problems (https://github.com/thearn/webcam-pulse-detector). We developed our own solution, involving (among other things) pixel-accurate facial feature detection and filtering methods not subject to FFT's regularity assumption

There's now a blog post with some analysis on this: https://hearty785.wordpress.com/

This is awesome. I fear how accurate it might be, though. Even if the technology is accurate (i believe it is), this, like most things with this presidential campaign, seems prone to fudging.

how do we know whether this is true or not?

You can try the algorithm yourself if you scroll down, then double check with your webcam and your own pulse ;-). Note that motion compensation is disabled for this demo, so it only works well if you do not move for a few seconds (the reason being that the pixel-accurate facial feature and skin detection algorithms would kill the server if 2-3 people try at the same time).