Furthermore, I don't believe that Fr. Chazal rejected Jorge Bergoglio as pope at the time of publication.

Because Fr Chazal makes a distinction between the spiritual papal authority (it's suspended due to heresy) and the material office (it's legit). Fr Chazal says he's not a pope in the spiritual sense, but he IS a pope in the material/govt sense.
You have this binary, black-or-white, all-or-nothing, view.