"such as the fact that their paper is published in a philosophy journal, and the guy having a history degree instead of a physics degree." -- argument from authority, very unscientific. If an unemployed poodle shaver publishes a replicable experiment, it is science.
"naive rebellious spirit of HN that dictates that anybody can overthrow fundamental physics with an experimental setup in his basement" -- if the experiment works and can be replicated, they certainly can.
There's also a misunderstanding of scientific epistemology in your last statement. Theories are seldom overthrown, but they are often extended. Einstein didn't overthrow Newton -- he provided an extension. Newton's equations still work, but with a very tiny error that only becomes visible at high velocities or with unbelievably precise measurements unavailable in Newton's day. A theory is not an absolute dogma, but a model that is deemed correct within its context -- namely all data and experiments available at a given time. New data or new experiments can extend the context, requiring an extension of theory. If this effect is real, it would not "demolish" or "overthrow" relativity, but would likely require some sort of extension to the theoretical framework. Who knows? Perhaps such a thing could point in the direction of the elusive quantum / relativity synthesis?
I am skeptical (lower-case S) of this, in that I wouldn't really believe it unless the effect could be reliably amplified. So far that hasn't been the case. But I don't consider it at all psuedoscientific to try it out. Even if the effect is a result of something else, doing so will refine your skill at measuring tiny forces and possibly advance the field of experimental technique.
The character assassination and arguments from authority are completely unwarranted, and is a major reason I am not a Skeptic (upper-case S).
P.S. a tangent:
Part of why I think CS advances so fast is that the unambiguous nature of computer "experiments" leaves little room for arguments from authority or character either pro or con. Either something works or it does not. Politics -- that age-old enemy of truth -- are clearly irrelevant.