The judge was with a hunting party (sort of like being on a bus, but the intimate opportunities are more tangible on a bus) that included a party in the case. Calling for recusal in that circumstance is ... hmm, seeking a word here .... stretching, at best.
No, the whole motion for recusal was based on the fact they had gone duck-hunting together.
The (Bravo) Sierra Club assertions were garbage. It contended that the VP's integrity was at stake. Scalia pointed out that Cheney's political ramifications were not a SCOTUS concern. Also that he was going to rule on Dick Cheney's role as Vice President, not as an individual. He cited 83 cases before the courts presently where officials are named in their official capacity. SCOTUS will be asked to decide if the oil company participants were members of the task force, in which case FACA applies and the meeting need to be open, or if they were contributors.
He also demonstrated why public opinion, especially as expressed through newspaper colums based on false information, is no reason to consider recusal.