Although there are some truths to your ref... I believe it has been updated since 1988.
John Hagerman (UE) was (most likely): s/o Cornelius Hegeman (and Marytie Wiltsee/Wiltse), s/o Adriaen Hegeman (& Elizabeth Van Wyck) s/o Denijse (Dennys) Hegeman (& Lucretia (Grace) Dollen (Darling) s/o Adriaen Hegeman (& Caterlijn (Catherine) Margits/Catharina Margetts). Adriaen Hegeman (the progenitor of this family was b.abt.1624 Elburg Gelderland, Netherlands >Amsterdam>Midwout (Flatbush) NY.
The "Captain John" mentioned is the s/o John Hagerman (UE).
I have seen the ref. for Francis Hagerman - however, I have no idea who he was. (doesn't appear to be a son of Cornelius Hegeman. - He MAY relate somehow to John Hagerman's wife.... Jannetje (Jane) Hegeman/Hagerman,(she is likely the sib of John Hagerman (UE) who settled in Ontario...)however -I don't have any information that such is the case.