I think what I had in mind was similar to why Etymotic offers both P and S versions of the ER4 each with a different impedance. The gain switch on anything but high will put a resistor between the amp and the headphones or IEMs, effectively changing the impedance of the amp or the headphones as I understand it, which might affect the overall frequency response, depending on the headphones or IEMs in question. It's a tricky thing to be sure of the effects of by ear, as it changes the volume as well. I've thought of measuring the effects out of curiosity, but the only equipment here I have with a low enough noise floor requires special adapters for single-ended input.
The gain switch does vary the voltage feedback by different value resistors, but I believe in the DX100, these resistors are not in series with the headphone output, so the output impedance should remain unchanged regardless of the gain setting. I will confirm this with iBasso just to be certain.