I can only speak for the Army, in general terms.
Defense Logistics Agency (DLA) is reponsible for procurement of bulk and packaged petroleum products (as well as many other items like fuel). The procurements, for the most part, are based on lowest bidder and required performance of the product. When I was on active duty (1980's) in the Army, I saw petroleum products from nearly all the major US oil companies (Texaco, Chevron, Shell, Amoco come to mind). Today, quite a few "green" products are procured, due to the Executive Branch mandate to use a percentage of recycled products.
Some unique products may be procured from a GSA Schedule, too, but the bulk is procured by DLA contracts.