I don’t think these are free parameters in the same sense. Like, if one theory says that a hunk of metal actually is made of many microscopic grains of various

I don’t think these are free parameters in the same sense. Like, if one theory says that a hunk of metal actually is made of many microscopic grains of various sizes and orientations, where the sizes and orientations of these grains has an effect on the behavior of the metal, you don’t count the “the sizes and orientations of these grains” as free parameters, do you?