Baloney. DexIII quickly shears down to about the same viscosity as DexVI. So "thinner" isn't the problem.
Now I could agree that it is a high mileage unit so why rock your boat, but if it shifts crisply and engages quickly then service it.
DexVI is a huge upgrade in most cases. And a great car for cheap trans BTW, we had these in our stable when the kids were young.