I'm not following your son's reasoning. 4K video does indeed take different compression algorithms, but the OP is talking about 1080p (he calls it HD).
More likely the problem is the very software-driven nature of the current generation of 4K monitors for video stream processing. That Samsung, like so many other 4K displays, use a native 120Hz display and then use software to claim 240Hz-like motion resolution, and for 1080p there's up-sampling going on too, and, while I'm just guessing, I think what the OP is seeing is nothing more than inefficient software or an inadequately spec'd SoC.
Here's an article I was reading when I was working out lip synch with my new Roku:
http://www.consumerreports.org/cro/lcdtvs/turn-off-these-3-features-in-every-tv
(The Roku's problem was solved by new firmware, and even that release is not very good, with occasional pops and noises when switching between videos.)