They must have no understanding of the term "authentic Magisterium".
Please...explain the authentic Magisterium. Can you explain what the "non-infallible Magisterium" is?
Authentic Magisterium simply refers to the authoritative and official Magisterium of the Pope (or, in alternative contexts, the bishops). Church Law declared, for instance, that anything appearing in the Acta Apostolicae Sedis must be considered the "authentic and official" papal Magisterium. It's opposed, for instance, to the Pope teaching as a private person. Prior to organs like the AAS that would sometimes have to be inferred from context.
Within the authentic Magisterium you have some things that meet the notes of infallibility and some things that do not, thus the division within the authentic Magisterium between infallible and non-infallible.