OK, how about this:
Two thoughts.
If the Rigby flats first showed up on their percussion match rifles, could they have something to do with allowing the gunmaker to shave off minute amounts of metal in order to reach an exact maximum weight for competition? I am imagining the flats being filed on the leading/rounded edge to "fine tune" the weight.
Also, that weight is between the hands where it is more likely unnoticed.
Secondly, gripping on the flats may simply be a more rigid and true form of fixing the barrel in the lathe for turning and the machine for boring/rifling. This being of utmost importance in an accurate match rifle as opposed to a standard sporting rifle.
That's all I can think of...