According to a web page whose credibility I do not know, Dexron III starts with higher viscosity, but the spec allows the viscosity to drop to a certain level as the fluid is used. Dexron VI has initially lower viscosity than Dexron III and its viscosity will drop to a certain level too, but not lower than the level allowed in Dexron III spec. That is why Dexron VI can be used in transmissions requiring Dexron III.

Since GM does not approve Dexron III anymore, a Dexron III fluid available now has only the oil manufacturer's claim that they (the oil manufacturer, not the car manufacturer or the transmission manufacturer) recommend their fluid for Dexron III applications. In contrast, Dexron VI fluids on the market passed GM's test.

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1992 300D 2.5 turbo diesel. 319 k miles.
124.128 chassis, 602.962 engine, 722.418 tranny.