I think their idea is that you start with water as your shielding and as you consume it over time you replace it with waste products. Stuff that's high in hydrogen makes excellent radiation shielding.
You could have dedicated shielding, but that's heavy.
You could make your shielding dual-purpose. Material that serves another purpose could be put around the outside of the spacecraft and act as shielding.
Machinery doesn't work too well, because it needs to be in a particular spot to work, and there isn't enough of it, and the stuff it's made out of isn't the best material for shielding.
Food and water, on the other hand, you can store just about anywhere. It's pretty good shielding too. For a Mars trip, you need a lot of it.
However, it's consumable. Food might be good shielding at the start of the trip, but there won't be much left at the end. Fortunately, food doesn't disappear when eaten, it's just transformed. The transformed food is still just about as good at shielding as the original was.
I assume this is more or less the chain of thought that got to this point.
