The answers you cite contain the information you want. It may not be "accessible" enough without reading and re and re-re reading. I'll try to summarise what was said in those references and in many other places, but do note that this is a summary and lots of detail are available elsewhere.
A digital camera sensor tends to produce an output that is linearly related to light level. this does not have to be the case, and here may be advantages in doing otherwise, but that's the norm so far.
With a linear sensor, if you halve the brightness you halve the numerical "reading" or light level. If the 'reading' is 4000 at 100% of sensor max light level capability, then it will be 2000 at 50% of sensor max level,
and it will be 1000 at 25% of max
500 at 12.5% of max
250 at 6.25% of max
125 at 3.125% OF MAX
62 AT ...
BUT each halving of light level is equivalent to one stop, or one EV level. It's far more intuitive to think in EV units but it can be equally expressed in stops.
So the first "stop" of sensor range has a certain EV of actual brightness at the top of this range and 1 EV less at the bottom, and the sensor has max reading of 4000 and minimum of 2000 and there are 2000 "counts" across this or EV level.
Areas in the image which are one EV level less bright than maximum brightness = the second stop / EV level in the image and have light levels from 1000 to 2000 and a 1000 range
The third stop has light levels from 500 to 1000 and a 500 range
The fourth stop has light levels from 250 to 500 and a 250 range
This means that the first stop of exposure has many numeric values between its top and bottom levels. Noise of a given magnitude that is a certain percentage of its range will be an increasing percentage of the range of a stop as light level falls.
eg say noise was +/- 5 units relative to the sensors 4000:1 dynamic range.
In the top stop noise is 5/2000 = 1/400 = 0.25% of the range.
In the 2nd stop noise is 5/1000 = 0.5% .
By the time we are down to the 8th stop the dynamic range available
= 4000 /(2 x 2 x 2 x 2 x 2 x 2 x 2 x 2) ~+ 16 sensor steps, and the 5 units of noise are 5/16 or about 31% of the range. ie at the op end of brightness a given level of noise may have little effect but as brightness falls the noise double for every 1 stop decrease and the % that the noise is of signal variation doubles.
Translating this into practice - take a highish ISO photo where the image is starting to get noisy. Now look in the shadow areas - you will find that they are far more affected - in about inverse proportion to their brightness.
So - EV levels that are close to the top of the sensors maximum light handling level are less noise affected. It does not matter about what the light level is as long as it can be corrected in due course. Rather, we push all brightness levels up until the brightest level is almost clipping. This allows the lower levels to have as much sensor variation as possible.
Note that 5 stops was just a convenient range to consider - this effect of right shifting matters right across the range.
Film tends to have a logarithmic response to light so comoresses a wider variation of levels into a lower effective range.