What he's describing is a common application of the organic chemistry laboratory called water extraction. Same idea as bubble washing your biodiesel to get rid of the excess methoxide, or free sodium hydroxide and methanol. Sodium hydroxide (lye) isn't soluble in oils, but it dissolves readily in water. Any acidic component of WMO such as acidic combustion byproducts will dissolve in the water in preference to the oil. So by circulating water containing a base or a buffering agent like sodium bicarbonate (baking soda) in contact with the oil, you'll trap and neutralize the acidic "bad guys" from the waste oil. The water can be separated, unless you created an emulsion by mixing too vigorously, and discarded, leaving you with WMO that has had its acidic components removed.
Not to pick nits, but you add acid to bring the pH down, and bases like lye to raise the pH. I think he meant to say that if the water sample in the initial test indicated acid was present, then adding sodium hydroxide to the wash water would bring the pH up, not down.
Quinn