You need the closest one due to the palette being that small (consider that it's mostly one pixel per face, if you don't go for closest you'll get weird shading results). There are other things to change to get the actual colors to show how they should.
Anyway, glad to see it worked! I would like to know if you previously experienced similar issues with other sets of models made by other people (featuring one pixel per color palette, FBX and OBJ formats), since I'm still trying to figure out what the problem is.
Also, if you ever use my models in your final game (or WIP project), pls share it here so I can see, always happy when someone uses my stuff on their projects!