This is partly true. 'Branded' fuels, such as Esso, Shell, BP, Texaco, etc contain additional additives, such as upper cylinder lubricants, cleaning agents, anti-bug additives, etc. One of the reasons supermarket fuel is a bit cheaper, is that they don't contain these additives. Fact. They are added at the point of loading the tanker at the refinery. So it does depend on which white diesel you are referring to. I tend to run my car primarily on supermarket fuel (because it's cheaper), but every 3rd or 4th tankful, will fill up at Shell or Esso. You could achieve the same thing on the boat by putting a shot of diesel Redex in once in a while. This is even more important if you are using the engine on tickover for battery charging for long periods.
Also worth being aware that since the introduction of a biofuel element, the brown sludge bug has made its appearance. This cost the retail industry a fortune until they understood what was going on. The bug grows primarily at any fuel/water interface, so it's worth keeping your tanks full in winter, consider an anti-bug additive and/or a fuel polishing system. It is capable of clogging up filters in no time.