Supplements are not required while on the HCG diet because fat-soluble vitamins are absorbed through the intestinal tract with the help of lipids (fats). While on the HCG diet, the body is mobilizing fat stores and would still be able to absorb the fat-soluble vitamins because of the fat (lipids) released into the blood stream by the HCG. 

Fat-soluble vitamins are stored in the body tissue while water-soluble vitamins are not.  This means that one can reach toxic levels of fat-soluble vitamins more easily than one can with the water-soluble vitamins, as those are the ones that the body will expel via urine if they are in over-abundance.

Before beginning any supplement, please do some research – including talking to your doctor to verify that the supplement is right for you.