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Patch materials are basically equivalent to copying an existing VMT's contents and (optionally) changing some of the parameters in it. Patch materials don't conditionally change existing VMTs or affect the "base"/"parent" VMT in any way, and don't allow you to do anything that you couldn't do with a non-Patch material.
If you have two VMTs that are almost identical (e.g. different $BaseTextures, but the same $BumpMap and $Phong settings), then you could change one VMT to be a Patch material that uses the other VMT as a "base", so that the "child" VMT only has to specify the differing parameters ($BaseTexture) - automatically copying all of the other parameters ($BumpMap and $Phong settings) from the "base" VMT. This way, you won't have to manually keep the other settings synchronised/identical across multiple VMT files. This is the use case for a Patch material.
No. The example patch material uses the red material as a "base"/"parent", but uses a blue texture instead of the red material's default red texture.
In other words, you should be able to replace the Scout's blue body VMT with the example patch material, and have it still look correct.