Andrew,
Let's break it down in simple terms:
As you know (I'm assuming) any non-linear process creates distortion. Simple compression creates harmonic distortion. Limiting creates harmonic distortion. Other process create non-harmonic distortion.
Let's look at the simple case of compression. If you compress a sine wave you turn it more square. This means that you inherently add frequency content to it, and that harmonic content is harmonic - it is related to, in fact multiples of, the frequency of the compressed signal. If you compress a 1kHz signal you'll get some 3kHz, some 5kHz, some 7kHz, etc., the greater the compression the more of these you'll get. Limiting with a low threshold turns the sine wave almost square, so the frequency content is the same as a square wave of the same frequency.
Now let's take a troublesome scenario - let's compress a 5kHz sine wave in the digital realm. At every sample we analyze whether that particular sample is above the threshold, and if it is then we apply a gain reduction formula to it. In the end we have a compressed 5kHz sine wave. The harmonic frequencies represented by that sine wave are 5kHz, 15kHz, 25kHz, 35kHz, etc. and on up the line. The problem here is that we have a digital signal that represents digital information above Nyquist, no? How is that frequency content going to manifest itself when we put this signal through a D/A converter and an anti-imaging filter? The 5kHz will come out as 5kHz and the 15kHz will pass through as 15kHz, but the rest? Indeed, it aliases back into the frequency range.
The best way to solve this is to upsample the material to a higher sample rate first - perhaps up to 192kS/s. Nyquist is now 96kHz. Any frequency content created up to 96kHz does not alias, and when we downsample we legitimately filter that extra content out with a decimation filter. In the end, all that remains is 5kHz and 15kHz, and the aliasing byproduct of anything that exceeded 96kHz, which is likely so low in level that it is lost below the noise floor, no?
This is one of the main arguments to upsample non-linear processes, but it is argued that this is the least important reason. For a more significant reason think about the device inside the compressor that establishes whether or not a signal exceeds the threshold, and then read the article here about digital distortion:
http://www.cadenzarecording.com/papersIf you have any further questions about how this all ties together let me know.
Nika.