From your source:
There are some commercial vegan diets available which have synthetically made nutrients to replace those found only in animal based ingredients.
The discussion is about commercial vegan cat food, which had the nutrients cats need, just sourced without killing other animals. The science on these diets is still relatively new, but early studies are looking pretty good.
Publicly owned means owned by the government. You are thinking of publicly traded companies, which are non public companies that have opened up stock ownership to the public