Yes, 1 Is the correct issue, but represents an 'ideal' case as you allude to in 2.
There are two forms to watch out for -
The type in 1, where two visually different colours look the same to the sensor, and where two spots that visually look the same visually look different to the sensor. They are not correctable automatically at all. Quantization errors, etc are not the limitation, it is that the RAW file does not contain ANY information that would tell the software how to shift two colours relative to each other - either closer together or further apart.
This is why cameras don't have 'perfect' colour on the colour check patches under standard lighting. It would be easy enough to design a mapping under controlled conditions to make it come out essentially perfect, but it would probably massively distort the colour quality under other circumstances.
To get more accurate colour you need to either have more eye like CFA filters, or more CFA colours (4 or more different pigments, at the cost of other issues).
The ultimate would be a sensor with tiny pixels that are small enough that they can record the actual wavelength of individual photons as they arrive, and then increment R, G, and B counters for each image pixel by a different quantity that was a function of the wavelength. If they were small enough and the sensor processing fast enough, it would do this as photons arrived and clear it before (on average) the next one arrived.
