This result could change physics forever

One bit I think you left out that might make this clearer to us casual physics fans is that the same measurement on the electron (which is of course easier to do) agrees with theory to a greater number of digits and is considered the "most accurately verified prediction in the history of physics."  There is no reason to think, then, that the muon wouldn't also agree entirely with theory, unless it's larger mass is making it interact more strongly with an unknown particle or force.