It seems that we agree on the working principle (it was however a long time since "most meters" had a direct coupling to the incoming light).
The current generated by the incoming light is balanced against another running through the amplifier. If these two balances perfectly no current is running through the spool that moves the needle. The needle is in the middle (null) position.
If however there is a difference between the currents, this difference will be seen as a current running through the spool, generating a magnetic field that moves the needle accordingly. This by the way is linear and that is why the distance between the numbers isn't (but this is outside the discussion).
If a meter is electronichally faulty, this usually means that the voltage is not correct (using modern 1.5 cells in a camera designed for old mercury batteries fx). In this case no meter reading will be correct except total darkness (anything multiplied by 0 will still be 0).
If the voltage is correct but the amplification is wrong, the null position will work and the other settings MIGHT work depending on the change. If done correctly, and if the precision is high enough you can amplify the movement of the needle and be able to read a more exact result than otherwise.
This however relies on the precision of the original measurement (like enlarging a photo. At first more and more details will be seen but after a while it will only be a bigger and blurrier picture (a 50x enalagement will not reveal 5x more details than a 10x)).
I have, as I said, been using it like this for ten years and it really does show the right values, either at null or at +/- 1 stop.
The only difference being that I have a span of 2 stops divided in 1/9 stop whereas the normal meter has 6 stops divided in 1/3 stop.
I do, by the way not only use the null position. Usually I take a reading, put it in the null position, move the outer wheel to the nearest combination of f-stop/time and then read the offset on the needle.
If, by chance, this is the result of a fault I will not have it any other way.