I will offer potential elements of answer concerning aliasing (as an artifact from over-processing a source signal). It is bound to be a phenomenon occurring independently from the process you are trying to apply. Any plugin might generate some aliasing or artifacts in a broader sense.
As you process a source signal, the processor reshapes the waveform using quite simple maths (in the end, all the maths electronics can do is add or divide). Basically, a processor adds to the original signal the statistical signal that it thinks will compliment best the component you're trying to isolate.
In the case of BNR, it calculates a statistical image of the noise and will smudge the waveform where it finds that the original signal features a "picture" of the statistically accurate noise. The more you push it, the more it's going to smudge the waveform and it'll start critically eroding the signal you're trying to focus on and listen to.
In effect this creates irregularities in the flow of waves that, when played back, are not natural sounding. Aliasing is merely an artifact that generates a particular sound; as it happens, the artifacts are organized in such a way that you seem to hear this tin foil kind of sound (that's the most obvious example, although aliasing can exist at any frequency although I have reasons to believe it'll always appear gradually from the high-end of the spectrum).
As a final note, the aliasing effect also happens when you record a sound. You may have heard of the "Nyquist frequency" or "Nyquist theorem". It's simple physics: to capture a certain frequency correctly, you must sample its waveform at least twice per cycle. Say you can only record with a sample rate of 20kHz, you'll be capturing frequencies just fine until 10kHz, only you won't be able to reproduce higher frequency correctly. I'm even gonna draw a diagram that'll explain this simply :)