It's consistent, just confusingly worded in the abstract.
Among those of equal status (full professors) there was no gender difference for likelihood of co-authorship: women and men were equally likely to co-author publications with another full professor of the same gender.
You missed the next sentence:
In contrast, male full professors were more likely than female full professors to co-author publications with a same-gender assistant professor.
It's saying there was no difference in sharing with equal status partners, but men were more likely to share with 'lesser status' partners.
The study is pretty poorly founded either way though--they merely gathered a bunch of research papers, looked at who authored them, and drew their conclusions from that. No interviews, no experiments, no random sampling. All of their results come from individuals in the academic field. They made no attempt to find data from other professions. Maybe this is a phenomenon that only happens in academics. We don't know because they didn't study other groups, so the results doesn't really have any broad application.
Basically someone thought this amateurish study would make a good headline and rolled with it.