A plank style flying wing doesn't have either a fuselage or tail to use for stability so that's a red herring.

In the case of a strongly swept flying wing the rearward portion of the wing acts a bit like the stabilizer. That's why we put in washout in that area. And if we alter the sweep angle to "make the fuselage longer" by lengthening the wing it most certainly does affect where the CG needs to be located.

Going back to the plank style wing for a moment. Due to the lack of a stabilizer the balance needs to be located quite strongly ahead of the 25% MAC of the wing. Just try to balance back behind that and it'll be like flying an arrow backwards.

If we add a stabilizer at all and put it some distance behind the wing the allowable CG now shifts to some point aft of the 25% MAC. So isn't it reasonable to expect that the further back we shift that stabilizer or the larger we make it that the more the CG can move back? How else do you explain how free flight models with super long tail moments but smaller size stabilizer areas are able to still be stable with a 50 to 70% CG location?