SuperSymmetry and QED aren't comparable in any sense. SS has always been speculative; it's attractive for some amthematical reasons but not mainstream. QED is as mainstream in particle physics as you get. It's not too far off to call it "The Central Dogma" (as molecular biologists refer to DNA.)
But there's nothing in this article that indicates that QED is in trouble, only that photomeission wavelengths differ from those predicted purely by QED. A much more likely explanation than the BIG HEADLINE that QED "might" be wrong is that there are other energy effects not accounted for by the experimenters.
That doesn't grab headlines or generate grant money, so they aren't going to broadcast the more pedestrian (and likely) explanation.
Does QED allow for relativistic effects? I recall hearing at a theoretical chemistry conference, that the color of gold was due to relativistic effects on the inner electrons; presumably, using a similarly heavy highly ionized species to "mimic" helium by drawing in the electrons, would result in very high orbital velocity; hence, room for relativistic effects?
Cheers!