Diatoms are particularly relevant because this is how the varve layers were determined in Lake Suigetsu, from the layers of diatom fossils. The original claim is that there was a seasonal variation in sedimentation covering the diatom fossils, I am proposing the likelihood that there were tidal water table related die-offs of freshwater diatoms that produced the diatom varves.
"The radiocarbon in the leaf fossils preserved in the sediment of Lake Suigetsu comes directly from the atmosphere and, as such, is not affected by the processes that can slightly change the radiocarbon levels found in marine sediments or cave formations." http://www.sciencedaily.com/...ases/2012/10/121018141834.htm
As others have mentioned, they dated terrestrial organic material such as leaves, twigs, and even insects. They didn't carbon date the diatoms. What they used the diatoms for was measuring annual deposits. Each spring and summer there is a bloom of diatoms which produces a white deposit. In the fall/winter there is less diatom growth so the deposits are dominated by darker colored clays. Therefore, a white diatom layer and a darker clay layer makes one year. This is what it looks like:
So what they did was compare the carbon date of the terrestrial organic material to the layer defined by the counting of diatom layers.
Regarding the white layer , I assume this is from the increased concentration of shells. This particular lake system is incredibly close to the sea, and freshwater diatoms are susceptible to saline water. Why are you so certain that the white layers were not caused by diatom die-offs from increased salt water in the water table during spring tides?
What makes you so sure that tides would bring salt water into the lake and produce layers that exactly mimic annual varving in freshwater lakes? Moreover, how could such a process sort leaf and insect debris so that it exactly mimics the fluctuations in the 14C dendrochronology data and the ice layer data?