When I see discolouration of the wood with black and lighter areas, I personally refer to it as spalting, although I agree its usually as you say a reference to a (pleasing to some) effect seen in hardwoods when decaying. I've seen it on Beech particularly, but also Ash, Hazel, Oak and Sycamore. I used to sell a lot of it in my gallery, but it was always for INDOOR use, the wood already being on its way out, and needing to be kept dry or it would fall apart. Heartwood spalting fungi is the same fungus as your 'white rot' but its able to get a hold in the softer sapwood first. Apparently spalting happens in living trees, dead trees, sapwood and heartwood, and its the same fungi at different stages or times. Good explanation here (seems we are both right, Rankinswood).
http://en.wikipedia.org/wiki/SpaltingWhat we all seem to agree is whether you call it spalted or white rot, there are areas in poor davetb's bench that don't look over healthy and are unlikely to make it to the claimed '40 year' life. Resinous conifers like larch or some dense deciduous hardwoods like teak, oak heartwood or Sweet Chestnut have a long outdoor life, untreated deciduous sapwood does not, contrary to the makers claim.