I think this is key to understanding how the whole current court thinks, I think that they think that they are special and can handle what in a lower court judge they would deem suspicious and implying possible conflict of interest:

Lucius said that instead of going out of his way to choose a judge who did not have any ties to Kavanaugh, such as one nominated by Bill Clinton or Barack Obama, Roberts had added to the perception that the nine supreme court justices are above the law.

That perception was ingrained in her, she said, in 2004, when Vice-President Dick Cheney was revealed to have gone duck hunting in Louisiana with supreme court justice Antonin Scalia. Scalia later declined to recuse himself from a case involving Cheney.

“When I think of judicial ethics, I think of that moment with Scalia as an ‘emperors have no clothes’ moment, and the realization that there were no ethics rules that apply to those judges,” Lucius said.

For example, at the same time as this, Bader Ginsburg is a personally buddy with Scalia. And now Sotomayr and Kagan have publicly said they think highly of Roberts as Chief. I think that they would all deny unexposed conflict of interest as the day is long. Whether they trust Kavanaugh is another question. They don't do things for P.R. purposes for their own selves, they are all classic tenured over confident personalities, if they do P.R. it is for the benefit of the court as a whole in the public mind. I was very surprised at Roberts ordering the investigation of the claims and I don't suspect any funny business about the judge. These are not politicians, they don't act nor think like politicians.

Yes it appears arrogant. That's because they believe their role is to counter populism and the majority. It is what it is, it's our monarchical branch, so to speak.

We could change it to a more political, less monarchical branch by removing the lifetime appointment thing. I have not really thought about whether that is a good idea.

All just mho from past reading.