Unless we literally understand absolutely nothing about the world, most of our understanding of physics still has to be true. Planets obey gravitation exactly as they should, hundreds of thousands of observational experience conforms with relativity. This experiment would mean a great many observations should be VASTLY different. 60ns doesn't sound like a whole lot unless you start thinking on galactic scales. The neutrino burst emitted from SN1987A would have reached Earth four years earlier if it were traveling at the recently observed speeds. Maxwell's equations about electromagnetic waves are all completely wrong if c is really this value, so it would mean that we somehow managed to invent the internet and computers and lasers and whatnot while actually not knowing a god damn thing about how electromagnetism really behaves. It would be insane.