I can't speak for Charles and Julian, but perhaps they were referring to the fact that a deep sand bed fosters a greater biomass of denitrifying bacteria, and as such would benefit more from a carbon food source like high test vodka, than a shallow bed with fewer nitrate consuming pseudomonas.
Take a look at some threads about this topic, as it's a controversial subject. You are importing nutrients when you add a carbon source like vodka or glucose. Nuisance algae can quickly utilize this resource and you'll have bigger problems than nitrates.
The other problem with nitrate reduction via DSB is that you experience a "kick up" of nitrate to nitrite. Yes your nitrate is reduced, but a portion of it remains as a more toxic form of nitrogen (nitrite).
DSB discussions are like talking politics or religion, so I'll let you read up, and make your own decision.