The Gothamist here reports that Doug A. Kellner, co-chair of the New York State Board of Elections and a Democrat, now believes that the New York election law known as Wilson-Pakula does not pertain to presidential primaries. The Wilson-Pakula law says non-members may not run in primaries for other types of office unless party leaders let them run.
The Gothamist article mentions me, although that mention is not perfectly accurate. I did not say presidential primaries are controlled by federal law. They are controlled by state law. Here is a somewhat better story in Capital.