The muffin tin radius is an auxiliary concept within the framework of the APW-type of bandstructure models. It is first and for all a mathematical concept, where a sphere surrounding the atoms in the model, separates a region near the atomic nucleus where a spherical symmetry prevails, from the interstitial region where a plane wave description is used. From the physics point of view the muffin radius is arbitrary. You can give it any value, even 0. Overlapping muffin tine spheres are a mathematical nuisance. The price to pay however is numerical efficiency. Of course the practical choice has to be, the value where the numerics performs fastest. This has nothing to do with measurement in the sense of a usual experimental observation. From a lot of trial and error, a set of values can be obtained, where the numerics works fastest. If you call that measurement, let it be, but there is no real physics behind.