Stephen has raised an interesting point which is really the truth of the matter.There is no formula to any of this and many people try to over analyse it all.
Im convinced in the past that the actions were just beefed up to take the pressures needed for the rifle cartridges.As explained by McKay Brown,To extend the action backwards from the face is pretty standard stuff.I'm sure the actions were lengthened to reduce gape.If the action opens less its quicker to open and close on reloading.You will also generally find that rifles with a Dolls head,or Greener or Kirsten type bolt will be made without bolsters.The third grip will help to stop the face from rotating backwards when fired.Rifles such as an H&H or Purdey with the hidden bites have no mechanical means of stopping the face from rotating backwards so the bolsters are introduced at the root of the face to strengthen that area in the hope that it won't move.
Usually fixed pin boxlocks have a larger diameter crosspin because thay have the cocking limb pin running through them.The crosspin on H&H type rifle is really dependant on the action size but not overly large.The Rifle should be jointed onto the draw and this will hold everything together.This will take the bulk of the strain.Another place of added strength would be the thickness of the action between the lump slots and the cocking limb slots.This is considerably thicker on a rifle than a shotgun which really adds to the flat width as asked in the original question.I haven't even mentioned back action sidelocks yet(Like the H&H) which is another strengthening method.
Sorry this answer is a bit all over the place.Double rifle action design is a big subject and at the moment I dont have time to write a lot about it.I hope this may answer a few questions and maybe sometime I'll have time to write a bit more about it.