Why is battery C rating not a function of battery topology/voltage?
You are miscalculating, or neglecting to calculate, the effect on the capacity of the entire pack of connecting cells in parallel. When you connect two cells in parallel, the current going into or out of them splits.  Assuming that the split is equal, then you get:

1S 4P: 3 V

3 V 3.2 Ah (9.6 Wh) 1C charge = 3.2 A.  Split evenly over four cells, 3.2 A = 0.8 A/cell


2S 2P: 6 V

6 V 1.6 Ah (9.6 Wh) 1C charge = 1.6 A.  Split evenly over two strings of two cells 1.6 A = 0.8 A/cell


4S 1P: 12 V

12 V 0.8 Ah (9.6 Wh) 1C charge = 0.8 A.  There's just one string, so 0.8 A = 0.8 A/cell



(As a practical note, you can't trust that a parallel arrangement will split the current evenly -- just be aware).