Let's put it this way: if you have high gain metal distortion circuit gained up to a 5mV clipping threshold, and then you roll down your guitar volume knob to play the blues, you're kinda using it wrong.
The point still stands that you can get the distortion effect, at the desired amount, at various places in the signal chain.
The problem you're talking about is about using too weak a signal and then using make-up gain. That can also happen anywhere in the chain.
I can reproduce the problem without distortion at all, using a clean signal chain.
Repro 1: turn down the guitar volume to simulate an extremely weak pickup. Then turn up the input gain to compensate. Result: noticeable increase in noise.
Repro 2: turn down pre-amp volume, and crank up power amplifier volume to compensate. Result: noticeable increase in noise.
Gains/levels have to be evenly distributed in the chain.
Sure, you will lose headroom if your intent is to have some soft distortion from the back-end of the amplifier, but you put a heavier distortion earlier in the signal chain. The heavy distortion masks the later one; it evens out the level so the headroom from the back is not available. There is a fix for that: you can punch that distortion in and out with your foot as needed.
- avoid noise early on in the change
- turn your guitar up halfway
If you want to avoid noise early in the gain chain, do not rob your guitar of signal by attenuating the output of the pickups with the guitar's volume. Now though that is done, by some players (and works for them), it isn't a way to get headroom or minimize noise.
You get the least amount of noise by keeping the volume of the guitar at maximum, and switching tones later in the chain. A clean pre-amp channel has much better noise characteristics than a dirty channel, and rolled down guitar volume control.
Seems like the bad noise in the case we're discussing would be what the tube circuit generated when it was not being intentionally driven to distortion... is that a correct interpretation?
Frequency components that are not in the original signal, but are only present when the signal is there are usually distortion.
(Why "usually": radio-frequency interference is noise. In audio, you may not notice RF when there is no signal. But when signal is present, it may mix with RF in a nonlinear way, causing additional distortion products attributable to the RF. I.e. the RF noise is "descends" into the signal's frequency range via intermodulation.)
e.g. If you have a diode clipping OD/Distortion circuit made out of some diodes with a Vf of 5mV as opposed to the 700mV of a normal diode, you would need to have a smaller input signal for an equivalent amount of distortion. That smaller signal has a lower SNR given some constant noise floor from thermal noise etc, and the SNR can only stay the same or get worse after you start amplifying it.