Oliver's three accomplices received prison terms ranging from five to 99 years. He got the death penalty, and in his appeals lawyers contended jurors improperly consulted Scripture that called for death as punishment for murder.
"The jury's use of the Bible here amounts to a type of private communication, contact or tampering that is outside the evidence and law," the New Orleans-based court said.
But the appeals court, in a ruling posted late Thursday, said it didn't see enough evidence to overturn decisions from Oliver's trial court and the Texas Court of Criminal Appeals that upheld the jury verdict.
"As Oliver has not presented clear and convincing evidence to rebut the state court's finding that the Bible did not influence the jury's decision, we cannot say that the jury's use of the Bible had a substantial and injurious effect or influence in determining the jury's verdict," the 5th Circuit said.
The court last year upheld Oliver's conviction and denied his request for a federal evidentiary hearing on the Bible-related claims but agreed to consider arguments on the matter.
At issue was a passage in Chapter 35 of Numbers which, in the New American Standard Bible, reads: "But if he struck him down with an iron object, so that he died, he is a murderer; the murderer shall surely be put to death." Other versions of the Bible have similar passages, some referring to an "iron rod" as the weapon.
The victim in the case, Joe Collins, was shot and then struck with the barrel of a gun, which Oliver's lawyer said could be likened to an iron rod.
"You could say God and Moses anticipated this exact thing if you take a literal view of it," Winston Cochran said, discussing the case late last year. "And that's got a lot of potential for mischief."
Cochran could not be reached Friday. A voice mail prompt at his phone would not take a message.
Prosecutors had argued there never was an implication jurors voted based on Scripture or had any kind of religious discussion.
Collins went out to pick up a hamburger for dinner in 1998 and returned to his rural home to find Oliver, then 20, and 16-year-old Benny Rubalcaba inside. Rubalcaba's 15-year-old brother and Oliver's girlfriend were outside waiting in a pickup truck.
As the two intruders tried to run away, Collins got a rifle and shot Benny Rubalcaba in the leg. Oliver fired his pistol at Collins, then grabbed the man's rifle and beat him with it, evidence showed.
One of the teenagers later would say he saw Oliver swinging the rifle at Collins like a golf club and then like an ax. The fatal wounds to Collins' head and face left him nearly unrecognizable and with severe skull fractures.
Evidence showed Collins was shot five times by Oliver, with at least two of the shots fired while the man was laying on his back on the ground outside his house.
A neighbor found Collins dead in the front yard. Collins' hamburger was still in a bag on the front seat of his pickup truck.
The wounded Rubalcaba, taken by his friends to a hospital, eventually told police details of the attack. Oliver was arrested in Houston with his girlfriend.
Defense lawyers interviewing jurors after Oliver's capital murder trial discovered jurors had Bibles with them during deliberations.
At a state district court hearing two months after the trial, four jurors testified about the Bibles in the jury room and gave varying accounts, ranging from one Bible to several being present. One juror testified they had them because they would go to Bible study following court proceedings. Another said any reading from the books came after they had reached a decision. A third said the reading of Scripture was intended to make people feel better about their decision.
"There is contradictory evidence regarding whether the jurors' consultation of the Bible occurred before or after the jury reached its decision," the appeals court said. "Several jurors testified that the Bible was not a focus of their discussions."
The court also noted the trial judge had instructed jurors to not refer to or discuss anything that wasn't in evidence, and that the jurors brought the Bibles on their own and without the knowledge of the judge.
Oliver does not have an execution date.
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