I won't try to debate what the Lyman manual has to say, and didn't read your question with that in mind. However the Lyman manual is a compilation of many writers articals, so controversy and fiction which the author doesn't have to stand behind is certain.
I wrote Jacketed Performance with Cast Bullets so readers could follow one author from beginning to end, and have a live person to question if he has problems or questions. So readers get results without confusion, which isn't needed with the already complex science of making lead bullets work.
I like their flux recomendations, preferring cheap lard purchased at the grocery store to anything I have tried. It does smoke, same as all grease type fluxes, beeswax, etc, but if you don't have adaquate venting to take care of that, move your operation to where you do, or you'll be soon sick from the fumes. I definately recemmend against using Marvalux, (Which seems good because if produces no smoke), because it leaves a heavy residue on the pot walls and skimming dipper. I like a large kitchen spoon to skim, and if the skimmer or ladle isn't heated good and hot the moisture it contains after laying on the bench for a while, will cause lead to blow up out of the pot causing nasty burns. I got it once and that should be enough for all the world!!
After fluxing, nothing in the skum left on top can be put back into the alloy. Throw it out. If using a bottom pour pot, leaving a layer of residue on top has no effect on the alloy comming out the pour spout, but it can exclude air from the top of the melt and minimize oxidation, which will minimize the need to flux. With a bottom pour pot, don't worry yourself about fluxing often. Keep the pot at least 1/3 full or topped off and don't stir it, and you'll get perfectly clean bullets even with the top covered with dross. I flux after perhaps 40 hours of operation, or when bullets returned for remelting tend to float on the skum, and bullet quality is just as good as if I fluxed frequently.