I think that SoulSurvivor is right on target. After I started getting the benefits from oil pulling, I wanted to understand how it worked too. From my reading, and my own knowledge, I agree that the oil is indeed "pulling" from the body.
There may very well also be enzymes involved ... in fact,it stands to reason as holding anything in our mouths activates enzymes.
Interesting note: what is used in natural cleaning products (ie. laundry soap, dishwasher detergent, liquid dish soap, etc...) to make them work? What is it that allows them to clean?
Fatty-acids. It is the medium-chain fatty-acids which attract or draw dirt, debris, bacteria, etc... to themselves. They are called organic "surfactants"; when my wife and I make laundry soap for example, in addition to some mineral based "scrubbers", we always melt down a bar of vegetable based glycerin soap: vegetable oil. So, it stands to reason that the same stuff that cleans clothes, dishes, etc... will also clean the "dirt" from our bodies.