Well OP does stimulate the liver. It's like a small liver flush. So with food in your stomach, there could be some issues. I think that's why it's better to do this on an empty stomach, and that's what originally was said to do with Dr. Karach.

I have known of people to OP on a full stomach with no problem however.

Personally I do it as soon as I get up. I want to get rid of whatever was building up in my mouth over night, and spit out it as soon as possible.

I did oil pull once with a full stomach. I then proceeded to throw up all the contents of my tummy-and the oil never triggered my gag reflex. So there is definitely a reason for that rule, although why exactly it happens I am not sure.

Saliva contains enzymes...specifically amylase (for digesting starches) and lipase (for digesting fats. When you oil pull on an empty stomach, the lipase is available to emulsify the oil you are swishing in your mouth. Emulsify means to break down into tiny pieces. SO oil pulling on an empty stomach means the salivary lipase is available for the oil pulling, and the oil can therefore get into all the little cracks and crevices in and around your teeth. If you do the OP after a meal, the enzymes have been used up and it takes close to 5 hours for the digestive enzymes to re-organize for the next meal. If you are SURE that you are abundantly blessed with vast quantities of digestive enzymes, you can get away with OPing after a meal. But nowadays, most people tend to run a little shy on digestive enzymes rather than having an overabundant supply. I recommend being conservative and doing it on an empty stomach.