Saying "Equifax Data Breach Settlement Administrator" (taken from equifaxbreachsettlement.com) instead of "Equifax settlement team" (used in the article) doesn't seem appreciably different.
I agree those two aren't appreciably different. They are both bad if the writer doesn't make it clear that the team (no matter the name) isn't in the employ or under the influence of equifax in any way.
I guess I just put more responsibility on Equifax itself even if these actions were through an intermediary of theirs. This makes me think of the Tylenol tampering in the early 80's [1]. Johnson & Johnson's response wasn't court mandated (what doesn't seem to be mentioned is that it wasn't just a targeted recall, but a wide recall encompassing unaffected product in order to regain trust with consumers) Equifax chose their response to be court-mandated and minimal. Someone chose this representation that's creating additional hoops.
I'm glad to see them citing sources properly. I can understand your concern they're not emphasizing the right party, but I don't think that would really help. Most people think class-action settlements are a joke, which means they don't have faith in the legal system. If Equifax feels like their reputation is damaged after fulfilling their legal obligations, they're free to do more.
I understand Equifax did not hire the Settlement Administrator. I still see Settlement Administrator as an intermediary for the Equifax legal case. Like you are saying, the parties here are the plaintiffs, defendants, and the legal system. I feel like focusing the Settlement Administrator just diffuses blame (for all we know they are just following the terms of the agreement). I think the article appropriately focuses on Equifax and how poorly the legal resolution is playing out.
I agree those two aren't appreciably different. They are both bad if the writer doesn't make it clear that the team (no matter the name) isn't in the employ or under the influence of equifax in any way.