the reason why I suggested to use floats is that floats have a much larger dynamic range than integers. In particular, if the values created for the Background in DBE are very small (i.e. in the order of 1/(2**16) in float terms, or <1000 in integer terms), you get posterization with integers. Floats handle this smoothly because values are scaled by an exponent.
Your are right, STF does not influence the result. But apparently it is less accurate then a full Histogram Transform, presumably to be fast. I have also seen cases where STF cause posterization, but with HistogramTransform everything was fine.