An understanding of how the systems work will help you understand why some people believe this.
A moving fader automation system, while quite expensive, is in some respects very simple. Essentially these systems utilize special audio faders with servo motors attached to them. When the levels are being controlled by the automation system the motors simply set the fader to the correct position and viola, you have your mix. Your audio signal doesn’t pass through any electronic components it wouldn’t normally be going through.
The lower priced alternatives to moving fader systems have been VCA (Voltage Controlled Amplifier) systems. In these systems there is an additional gain stage (the VCA) in the audio path that can be used to turn the level up or down. The channel faders themselves may or may not even have audio passing through them. In some systems the fader is just used to control the VCA, while in other systems the audio passes through the fader on its way to or from the VCA circuit. Either way the VCA is controlled by the automation system and that system is programmed by the actual fader, or in some cases there are separate faders for setting the automation levels. So you tell the automation system the levels you want by your fader position (there’s a circuit attached to it that reads its level) and then the automation system uses the VCA to control the level. VCA based systems are usually more complex to use because the faders don’t move along with the automation. Instead there are separate screens and/or LED indicators to show you where the VCA is in relation to the physical fader position. As complicated as it sounds these systems have historically been less expensive than their moving fader counterparts, which still require computers and most of the other electronics (along with the expense of the motorized faders themselves).
In some of the VCA based systems it is possible to bypass the VCA leaving only the regular fader to control the level. The reason engineers would want to do this – and here’s where we get to the answer to your question – is because the extra VCA gain stage does color the sound of the audio a little bit. It’s not as “transparent” as simply running your audio through a resistor (which is essentially what a fader is). So some engineers prefer to bypass this circuit while they are tracking, and then engage it only for mixing. This is why moving fader systems have historically been considered sonically “better.” This, however, is mostly perception based on the past performance of such circuits. In recent years VCA technology has advanced to a degree that there is very little sonic downside to using them in a mixer. In fact, some currently available mixers with “moving fader” automation still use VCA’s. The fader does not pass audio; it is only used to control the VCA, and moves to show the automation level. These systems cost less to produce than a “true” moving fader (with audio in the faders) system, but still give the user all of the ergonomic advantages associated with moving faders.