Probably because they had flags on the S-IC, and that was the biggest and baddest of all the stages. Not sure.
This actually makes technical sense. Since the S-IVB goes into the same trajectory as its payload, every kilogram of mass you can remove from the S-IVB means a full extra kilogram of payload it can carry. An extra kilogram of payload would have required removing 5 kg from the S-II or a whopping 14 kg from the S-IC.
Considering how hard Grumman had to work to shave ounces of weight from the LM, even the weight of the paint in a logo must be considered.
Those who were around for the first two Shuttle flights may remember white external tanks. Starting with STS-3 they went orange - the native color of their polyurethane insulation - when the white paint was omitted to save quite a bit of weight. Because the tanks went almost to orbit, the reduction in tank weight turned into a nearly equal increase in payload capacity. Similarly, moving the painted logos from the S-IVB to the S-IC on the Saturn V would increase payload capacity and/or allow much bigger logos. And why not, since they can only be seen on the pad and in early flight when all three stages are still together?
Unmanned launchers often feature multiple logos on their payload fairings, but because they do not go all the way into orbit (usually being jettisoned shortly after stage 1/2 staging) the effect of the extra weight is more like that of a logo painted on the first stage.
