The apple juice (or apples, or apple cider, or apple cider vinegar) is for the malic acid content, which helps soften liver/gallbladder stones & debris. Hence we usually see this for the 'prep stage'.
The citrus has an entirely different purpose. The citric acid
in the citrus juice creates contractions in the gallbladder - hence assisting the flush procedure.
Everything 'technical' that we EVER want to know if found here: http://curezone.com/blogs/f.asp?f=1196
in Telman's Blog.
However, let it be known (in my body) that I have done two flushes where I was so focused on the olive oil and laying down afterward, that I totally FORGOT to drink my grapefruit juice. Both flushes were VERY successful. This does not mean I'm suggesting to flush without citrus, only that whatever effect it has, seems to have made little or no difference in my body on those particular flushes.
Enjoy dat Superfood - it's like water to dehydrated sponge! :)