Consequences of Undecidability in Physics on the Theory of Everything

Neither Physics nor Computability are my field, but this seems like a circular argument or perhaps just fallacious: If they aren't proposing some experiment the result of which should prove or disprove simulation, aren't they just drawing conclusions from a potentially invalid set of mathematical assertions? iow is it possible to deduce something about the physical world simply by rearranging mathematics? And they seem to be saying that nobody has provided a mechanistic relationship between various realms of physics, therefore there isn't one, therefore it can't be simulated.

If someone asked me to figure out a way to prove that a program I'm running is inside a VM or not inside a VM, I don't think I'd begin with reading the programming language manual...I'd be looking for observable differences a program can detect to tell if it's virtualized.