The rest of the Supreme Court? Sheesh, these people are split seven ways from Sunday. The appeal had to go to Anthony Kennedy. He has jurisdiction over emergency appeals from that area. We have no idea how he handled it. Did he just dismiss it himself, or did he ask others if the wanted to hear it, and if so, who said what? All we know is there were not at least four(the minimum number) justices who agreed to hear it. Judge Bork told Sean Hannity that he predicted they would not hear it if for no other reason than the federal law that was passed giving her parents federal court access was about only Terri, not a general class of people, and that the Court does not and would not agree to hear an appeal about one person.
I think the last part of your statement is correct (class of people vs individual). For whatever reason, the Court was comfortable letting the lower courts' opinions stand. And remember, the federal appealate court had 2 REPUBLICAN appointees that found in favor with Greer's decisions and a democrat who dissented. Interesting.