There is no dispute about this basic fact in the death penalty case the Supreme Court will hear on Wednesday: On a chilly morning in January 1997, in Room 102 of the Best Budget Motel in Oklahoma City, a handyman named Justin Sneed beat the motel’s owner to death with a baseball bat.

The rest of what happened is murkier. In exchange for a life sentence, Mr. Sneed testified that the motel’s manager, Richard Glossip, had commissioned the murder of its owner, Barry Van Treese. Based on that testimony, the only direct evidence linking Mr. Glossip to the crime, he was sentenced to death.

Last year, prosecutors disclosed long-suppressed notes that undermined Mr. Sneed’s testimony. They helped cause Oklahoma’s attorney general, Gentner Drummond, a Republican, to ask the state’s highest court for criminal matters to throw out Mr. Glossip’s conviction and order a retrial.

Lawyers call such requests “confessions of error,” and courts ordinarily give them great weight. But the state court refused.

In an unusual alliance, Mr. Drummond then joined lawyers for the inmate to ask the Supreme Court to step in to prevent what they said would be a grave miscarriage of justice produced by flagrant prosecutorial misconduct.

Mr. Drummond said his stance had come with a political cost.

“I’ve been criticized by prosecutors, attorneys general and politicians,” he said in an interview, “and that really has absolutely no bearing on my commitment to the rule of law. And if at the end of my term the citizens of Oklahoma would prefer to have a politician, as opposed to one who’s going to follow the law, then they have every right to elect that person and remove me from office.”