As far as I am aware the main reason for using lightproof containers is to protect the flavour. And in my experience this is true, milk from transparent containers often has an 'off' taste.
But because Anchor made claims about vitamin levels, Consumer compared vitamin levels in lightproof containers against levels in transparent containers and found no difference.
Anchor removed the claims regarding vitamin levels, even though there is research that shows light degrades vitamins in milk.
https://www.ncbi.nlm.nih.gov/pubmed/26874418
The comments in the stuff story are interesting. It just seems that so many people cannot tell when milk has an 'off-taste'.
This used to happen quite often when we bought transparent containers but never since we started using the light proof containers.