IIRC, one theory is that in the horizontal position, all tissue compartments are at the same depth and at the same ATA, and therefore offgas at the rate predicted by the model. (Not sure if this is what the author meant, as he specifically mentioned the lungs only. Plus deco theory can bring about some lively debates...)
In comparison, for a vertical position, some tissue compartments are at a higher ATA (deeper) than others, and thus may offgas slower than the model predicts. Since the model recommends the optimal depth for deco, these compartments below the optimal depth are not off-gassing optimally.
I agree with limk, the difference may not matter. Being vertical is approx 0.15ata difference from head to toe.
As a side note, deco theory also recommends a diver should be relaxed and comfortable during deco. So I think it's not that critical to be horizontal, especially if it adds noticeable stress to the diver. That may actually be worse off than being vertical.