Amicus curiae (“friend-of-the-court”) briefs are briefs written by individuals or groups who are not directly involved in a legal case, but have expertise or insight to offer a court to assist in making its decision.
In no way are they related. You seem to have not understood the definition. It's a latin phrase used to refer to writings submitted on behalf of a side in a court case as an ex parte expert on the subject at hand. It has nothing to do with lobbying or actual friends of court officials.
I think you are missing fully half of the story here.
If someone gives you lavish gifts, free luxury vacations, use of their private jet, all-expenses paid vacation cruises, you start thinking of that person as a 'friend', no?
In this case, 'friend of the court' clearly has double meaning because the amicus curiae is also simultaneously one and the same person as the billionaire gift giver I described earlier. In layman's terms, it's bribery.