So dropping them into windows explorer’s project folder does work, as you said, and the reason all of this happens (the textures having to be reassigned etc). This isn’t something you can alter, as this is because the files weren’t packed together to preserve references. That’s the fault of the sharer. Honestly I’m not sure WHY they wouldn’t pack it as an .fbx, .obj, or their native file type. Most websites do that, such as Mixamo.
Long story short, the reason the files aren’t linked is because you are importing them separately, which isn’t your fault because they weren’t packed efficiently. References aren’t saved when they’re not packed together, because otherwise you’d get Null Reference Exception city. 