I am not certain your argument holds for the system being considered here: it is important to mention that local energy conservation in a lab in flat non-expand

I am not certain your argument holds for the system being considered here: it is important to mention that local energy conservation in a lab in flat non-expanding spacetime is very much a thing. And flat non-expanding spacetime is where this experiment is being done. Sure, if you are talking about cosmology and GR then some new effects appear, but is it reasonable to talk about those here - I doubt that the sensitivity of the equipment warrants talking about those.