I am fully aware that the rarity of bipolar glaciation is a central thesis in that paper. But it still says that such a thing occurred repeatedly over the last 22 million years
No. You obviously are not aware that the rarity of bipolar glaciation is a central thesis in that paper. If you were you would not have been arguing against it or still claiming that it repeatedly occurred over the last 22 million years. You are still being dishonest. What do you not understand about the conclusions of the paper below? The study concluded that major bipolar glaciation at the Eocene/Oligocene transition is unlikely. The study concluded that no definitive evidence of widespread northern-hemispheric glaciation exists before ,2.7 Myr ago.
Thresholds for Cenozoic bipolar glaciation
"For major bipolar glaciation to have occurred at Oi-1, CO2 would first have to cross the Antarctic glaciation threshold (,750 p.p.m.v.) and then fall more than 400 p.p.m.v. within ,200 kyr to reach the Northern Hemisphere threshold (Fig. 4). Increased sea ice and upwelling in the Southern Ocean 13,29 and falling sea level 14 could have acted as feedbacks accelerating CO2 drawdown at the time of Oi-1.This is supported by CO2 proxy records and carbon-cycle model results showing a drop in CO2 across the Eocene/Oligocene transition10,13,14,
but none of these reconstructions reach the low levels required for Northern Hemisphere glaciation. We therefore conclude that major bipolar glaciation at the Eocene/Oligocene transition is unlikely, and Mg/Ca-based estimates of deep-sea temperatures across the boundary 5 are unreliable. Our findings lend support to the hypothesis that the 1-km deepening of the carbonate compensation depth and the associated carbonate ion effect on deep-water calcite mask a cooling signal in the Mg/Ca records 4,5. Therefore, the observed isotope shift at Oi-1 is best explained by Antarctic glaciation 22 accompanied by 4.0 uC of cooling in the deep sea or slightly less (,3.3 uC) if there was additional ice growth on West Antarctica (see Methods and Supplementary Information). This explanation is in better agreement with sequence stratigraphic estimates of sea-level fall at Oi-1(70 620 m)19,20 equivalent to 70–120% of modern Antarctic ice volume, and coupled GCM/ice-sheet simulations showing 2–5 uC cooling and expanding sea ice in the Southern Ocean in response to Antarctic glaciation 29. Additional support for ocean cooling is provided by new records from Tanzania 16 and the Gulf of Mexico 15, where Mg/Ca temperature estimates show ,2.5 uC cooling in shallow, continental shelf settings during the first step of the Eocene/Oligocene transition.
In summary, our model results show that the Northern Hemisphere contained glaciers and small, isolated ice caps in high elevations through much of the Cenozoic, especially during favourable orbital periods (Fig. 3a–c). However, major continental-scale Northern Hemisphere glaciation at or before the Oi-1 event (33.6Myr) is unlikely, in keeping with recently published high-resolution Eocene no definitive evidence of widespread northern-hemispheric glaciation exists before ,2.7 Myr ago, pre-Pliocene records from subsequently glaciated high northern latitudes are generally lacking. More highly resolved CO2 records focusing on specific events, along with additional geological information from high northern latitudes, will help to unravel the Cenozoic evolution of the cryosphere. According to these results, this evolution may have included an episodic northern-hemispheric ice component for the past 23 million years."