Certainly, let me use an analogy which might help. Lets say you are recording a violinist onto a tape recorder using a high quality tape. When the violinist plays softly you have to amplify the signal to increase the volume. As you do so you also increase the noise from the tape. Maybe the violinist is playing so soft that their sound level falls to the point where it's difficult to tell if it's a violin or tape hiss (noise). Depending on which tape you use (high quality or cheap quality) and what equipment you are using (radio shack tape deck or Yamaha digital tape deck) you will have more or less noise when recording that violinist at the same recording level.
This also holds true for image sensors. When the brightness is low such as in a shadow or low light situation the photon levels are so low that they are mixed with noise. Depending on the sensor and supporting backend electronics there may be more or less noise. Amplification, same as with that tape deck, amplifies not only the photons but also the noise level. Higher quality components (better sensor, larger pixels, better amplifiers) can all contribute to less noise compared to the signal and more DR in the shadows.
You absolutely cannot compare sensor IQ without also considering the supporting electronics used in processing the signal. Even if the cameras use the exact same sensor, different electronics on the back end will affect the IQ. There are a lot of different points to consider. What causes IQ differences in 5D3 and 1DX may be different in other models depending on the generation of support electronics also used.
Remember also that the image as it hits the sensor is still analog. It's not converted to digital until after any amplification has already occurred.Failure of the amplifier to pull photons from the background noise.
Please explain what you mean by this statement.
Not even close to explaining your statement which was (and I'll add some emphasis)... "FAILURE of the amplifier to PULL photons from the background noise". All you've done is tell us with your analogy that for low signal levels the SNR would be high. Please enlighten us how even the best amplifier in the world, even a hypothetically perfect amplifier, will "PULL photons from the background noise".