Usually the military makes good decisions, but......
Army intelligence is an oxymoron.
Keep in mind that if they are using one, it's from the lowest bidder.
Mindless homilies aside, it's unlikely to see a brand-name product in a motor pool supply. The product might actually be there, but in DOD or Army packaging. It might be supplied by the lowest bidder, but it might also be a sole-source item (one situation where the product might be in 'civilian' packaging).
As part of the purchase contract, vehicle and equipment suppliers specify the lubricants and additives required for their equipment. And they frequently specify lubricants right off the military's list of available lubricants). If a supplier specifies the use of something not on the list, a technician or engineer at Tank and Automotive Command will try to match it to an existing DA or DOD product (Lubricating Oil Type 7 Mark 3, etc) - the military's list of available supply items is extensive. If a product absolutely can't be matched, the TACOM tech folks should go back to the equipment vendor and ask if they can recommend a substitute product (or even if the product is really necessary at all). Since most military vehicles are supplied by large defense contractors, this situation doesn't come up every day.
Putting something non-spec in the oil or using non-spec oil or grease of a military vehicle is greatly frowned upon - a good way to get fired (for civilians) or seriously disciplined. Lubrication Orders are rather strictly followed. When the IG or a tech inspector makes his periodic visit, compliance with LOs is always checked (and it's not a good thing to have some odd-ball product sitting on your supply shelf).
With UOAs in use on just about every piece of equipment, putting in a non-spec additive should be detected. Granted, a pint of 99% mineral oil Z-Max in the sump on your M939 5-ton truck may not be detected (by either the IG or by the vehicle). Tank and Automotive Command should get digital copies of most UOAs. I don't know if these UOAs are analyzed by computer (likely) or by a clerk, but it would not be difficult for a computer program to scan and highlight unexpected readings found on a UOA.