It's the researcher who produced and typeset the article; the publisher does nothing more than hosting PDFs sent directly from the authors after they passed peer review, which is not something the publisher is involved with.

This is false. If all they did was host pdfs everyone would just use arxiv.

See http://www.nature.com/news/open-access-the-true-cost-of-scie... for a good overview of all the sides here.