I was wondering the same thing myself. Then I came across a totally unrelated article about how scientists are learning to diagnosis Breast Cancer and other diseases by examining the enzymes in saliva. Evidently there are over 50 different enzymes in salvia many of which correspond to disease. This made sense to me in explaining how oil pulling might work, if it is pulling toxin out though this sophisticated enzyme system.
As for the “empty stomach” question, (I believe) it is necessary because just as your body will cause you to water at the mouth when you are hungry; the initial onset of pulling on an empty stomach will elicit much more salvia and thus more of these enzymes….at least that’s how I see it.