My suspicion is that like the MOV files generated by the GH3, a GH4 set to 0-255 will create files flagged as full-range. THese should be interpreted correctly without clipping either blacks or whites, and help to reduce banding as you have 256 possible values not 220.
However, I guess Panasonic is not flagging clips as being full range if either the blacks, or the white are set at 16/235 respectively. Therefore the default 16-255 setting is not flagged as full range in the files, and is being interpreted as 16-235.
Just a hunch though.