Ford or any other manufacturer can not deny warranty solely based on the use of a particular product such as oil brand or filter. This is part of the Fair Trade Act of 1984 by Magnuson and Moss. It applies to any consumer product sold in the US, whether a US car company or one from Europe, Japan, etc.
However, warranty can be denied if the use of that product leads to the direct failure caused, ie if you use a 20W50 oil in Chicago in the dead of winter and cause upper engine wear due to lack of lubrication on startup and the mfg recommended to use a 5W30 for example, if I was the service manager and could document this, I would deny warranty.
Whether it was brand X or Y, and it is of the correct type (gasoline / diesel version) and the correct grade and it has documentation that it meets the appropriate API License (www.api.org will show you all the licenses for oils world wide), you can not be denied warranty "solely" on the use of a particular brand.