This Docking Station inherently does not reduce the gain per se, but just like any preamp, it has an output voltage swing limit of around 0.7V (I've measured with 1 kHz sinewave as an input) before it starts distorting the sound (clipping the waveform). So when the button is pulled out, it works as signal follower buffering it, whatever comes in, gets out, but up to 0.7V. You can reduce the output swing to zero (very convenient), but you cannot amplify the signal per se, the max gain is 1.
When the button is pushed in (passive mode), the buffer is bypassed and the input signal is directly routed to the output, and there's no restriction of the amplitude, if 3V comes from your piezo pickup, the same 3V will be at the output jack, just un-buffered. So, in your case you likely had input signal exceeding 0.7V in active mode, so you had to reduce the gain ("volume") to avoid distortion, while in passive mode there was no limiting, thus perceived "gain reduction".
I've played EUBs for 6 years now - first Stagg and later - MK Bass, but my background is actually in electronics engineering, so I understand all this impedances, bandwidths, roll-off frequencies and all that stuff. The MHz, dBm, CMRR or THD is far more comfortable terminology for me than Ionian, Dorian, Phrygian or Lydian, which is still Greek to me. My point is - I trust my instruments, measurements and conclusions. I sure get it that ultimately what matters to a musician is what the instrument actually sounds like to his/her ear, but knowing how stuff actually built and works never hurts, and allows me to avoid wasting time and money in searching for something some people (incl. advertisers) swear by, but it makes no sense from electronics fundamentals point of view.
I did not bother to take the Docking Station apart and reverse engineer the circuit on its tiny round PCB inside, just had its cover off and inspected it visually. It's built well. It's got about $15 worth of components inside, I'd say machining the enclosure cost quite a bit more, but as with everything, the value of a unit to the musician 'course does not come from [just] part's worth+profit margin. I have clear enough idea how this unit works, so there was no need for digging into the circuit deeper. But If I ever stumble across another (even non-functional) unit, I might take it apart and reconstruct the schematic out of curiosity, just like I did with the Stagg EUB preamp - another fun project...