simulation of lin-log amplification
The distribution of the log magnitude output of a log amplifier would be according to the log of the magnitude of the input. Although in implementation the log amp is not simply taking a log of the input signal, the result is indeed the log with reasonable accuracy (typically linear to the log scale within a fraction of a dB). Below shows how this should appear for both Rayleigh and Ricean distributions. Given the OP is not seeing the same skewness as is the case for the Rayleigh at the log magnitude output of the log amp, I would conclude that the input signal (which he does not have access to) was not Rayleigh distributed.

Notice the skewness decreases significantly as the dominant path in the Ricean distribution (A) becomes more prominent, as would be expected.