Oil pulling does not kill bacteria. Have you ever opened a container of rancid oil? The rancidity is caused by bacteria.
The theory with regard to OPing is that there is a vein (not an artery) that runs under your tongue. By swishing oil around in your mouth for 20 minutes (the time that it takes to fully circulate the blood throughout the entire circulatory system), OIL-SOLUABLE toxins are absorbed through the vein and discarded when we're done with our pull and spit the oil out.
The Seasalt water rinse following the pull is what kills bacteria, along with following up with a NON-flouridated cleanser: 100% pure olive oil; 100% pure baking soda; and the like.