You might have missed high temp super conductivity entirely then. The phenomenon was measured and replicated in many labs - but it was at least a few years before any plausible theory came out - and 20 years on we do not have firm agreement on the cause.
Poor comparison. High-Tc superconductivity was a demonstration of a known phenomenon (zero resistance current) under new physical circumstances. A better comparison might have been the photoelectric effect, which really had no explanation under the then-known laws of electromagnetism. The explanation for the photoelectric effect in fact did require a deep and radical revision of the basic laws of physics: Quantum Mechanics. Sometimes this happens.
These guys have not measured something which clearly requires such a revision of physics, yet they are full of breathless claims about its significance. Red flags all over the place.