It's worth pointing out that we're looking at more like 0.65c, through optical fibre. This would also be ignoring routing infrastructure/processing time and network prioritisation.
Fiber optic cables may not be able to penetrate the molten core of the Earth, but there is no law of physics that prevents information from traveling through the core of the Earth. Compare this to the speed of light, which is an absolute upper bound on how quickly information can propagate. There is simply no way, in this Universe, to do better than the straight-line distance through the center of the Earth.
