Paul, Thanks for raising this issues. You are not the only descendant to be led down the garden path. I'm also an Aussie Fernyhough descendant (from Thomas Fernyhough, military Knight of Windsor, via his artist son William who migrated to Sydney).
My mother's brother born c1910 had Furneaux as his middle name.The family erroneously believed they were descended from Captain Tobias Furneaux (who had some islands near Tasmania named after him). The myth perpetuated through the descendants, until I started my BDM research. The family even had old history books with marked sections which referred to Tobias, the sea captain.
I'm sure some people in the family still disagree with my research showing different origins!