People regularly report various kinds of "distortion" in sidechain-based effects. Sometimes it IS actual distortion of the signal path, but many other times it is really envelope ripple. We may think that an envelope extractor magically transforms our average signal level into some type of pure battery-like DC. But it doesn't.
Ordinarily, there is a tradeoff between responsiveness of an envelope extractor and its susceptibility to ripple. If it can react quickly, then any "jiggling" in the envelope as the string dies out will be more apparent. One can smooth out the envelope by a variety of means, but that generally results in a sluggish response to what you play.
Ripple rejection can also be managed by what is used as the control element. One of the nice things about photocells is that they generally don't respond super-fast. They essentially "ignore" quick fluctuations in the envelope voltage; much moreso than transistors or OTAs would.
Why does ripple sound like distortion? Because the envelope may be causing fluctuations in whatever parameter is being controlled. So, the envelope ripple in the Dr. Quack (especially as the note decays...which is NOT smooth) can produce "micro-filter-sweeps" at rates in the audio range. Imagine that the sweep of the filter were being controlled by a noise generator operating between 200 and 2000hz. Just constant buzzing little filter sweeps. To our ears it would sound very much like distortion. Same thing with limiters, compressors, and gates that can be adjusting the level by small amounts, very quickly.
I find that, for some devices, the best cure is to simply get in and get out quickly. So, a quick decay/release lets you avoid the ripple that seems to be much greater later on in the decay of strings. Another "cure" is to use full-wave, rather than half-wave rectification (the DQ uses half-wave). This not only doubles the speed/rate of the ripple such that it is not as audible, but also allows for smoothing out the envelope without necessitating annoyingly long decay/release times. Finally, if you can use a photocell, that's helpful too.