It sounds to me like the models your importing have no UV data, you should get hold of Lithunwrap, which is free, and load your model into that - it's a pretty decent UV mapper, and it'll even tell you if your model has no uv data.
If you imagine that all the UV coordinates are at 0,0 - so they're grabbing one tiny little bit of the texture, not even a full pixel, but the colour of that 1 pixel at 0,0 is repeated over the whole object because that's how the UV data has ended up.
But I'd say you should get hold of Milkshape or something, Truespace is not really ideal for game modelling, it's not great for texturing or low poly, Milkshape is much easier to use as well.
Van-B

Muhahahahaha.