Laterite or lateritic soils are not actually clay, as I understand the meaning of the terms. As I understand it laterite is very old type of clay, which has weathered from rocks, and been enriched with iron and aluminum minerals, and is very lacking in any nutrients for plants. Ordinary clay is also derived from rocks, so I'm not totally clear on what the differences are.
I think this is right. I get the impression that a lot of people are equating laterite with red clay, which isn't quite true.
Like Hoppy said up above, I remember a big fuss about laterite in the mid 90's or so, and that was before there were many (any?) commercially available plant-specific substrates, and a lot of people were just trying to grow plants in regular aquarium gravel.
Laterite is a heavily weathered soil found in tropical areas, pretty much everything that can be broken down or dissolved has been broken down and dissolved, so what is left is mostly iron and aluminum oxides. I think it's the combination of iron and being found in tropical areas is why it gained popularity in the aquarium hobbies (pure speculation on my part). Clays tend to be an aluminosilicate, and are usually a product of other silicates (micas, feldspars, etc.) weathering.
I also agree that if you go with a dirted layer in your substrate, or include iron in your root tabs or dosing regimen, it should be fine. Otherwise, I don't imagine it would be too harmful, but I think the benefits would be nearly negligible. (although, Walstad claimed a tank with both dirt and laterite showed symptoms of iron poisoning, so...)