In fact, attorney Dan Cogdell told jurors Wednesday, Graham wasn't even present at the murder.
Prosecutors say Graham and his fiancee, Diane Zamora, murdered Jones together on Dec. 4, 1995, because Zamora was infuriated that Graham said he'd had a one-night sexual encounter with the other girl.
Reporter Angela Hale of CBS affiliate KTVT-TV in Dallas-Fort Worth says lead prosecutor Mike Parrish admitted for the first time that they also believe Graham lied about having sex with Jones, but prosecutors stand by their assertion that Graham did commit the murder.
The crime occurred while Zamora and Graham attended different high schools in the Fort Worth area and months before Graham went to the Air Force Academy and Zamora to the Naval Academy.
They were arrested after Zamora confessed to a Naval Academy friend during a late-night dorm-room chat. Zamora was convicted in the slaying in February and is serving a life sentence in prison.
Graham, 20, also could face a life sentence if convicted of capital murder. Prosecutors are not seeking the death penalty.
The trial was to resume Thursday.
Cogdell and prosecutors agree that Graham telephoned Jones late the night she was killed and talked to her so long her mother became annoyed.
Prosecutors say the call was intended to deceive Jones, his cross-country runner teammate at Mansfield High School, into driving with Graham to the spot where he intended to kill her.
Graham's lawyers insist he phoned to warn Jones that Zamora was jealous, angry, and vengeful.
Prosecutor Mike Parrish said much of the evidence against Graham is contained in a confession Graham typed for police and Air Force investigators in September 1996.
Graham drove Jones to a lake with Zamora hiding in the hatchback of the small car, Parrish said. When they arrived, Zamora popped out.
As Jones tried to flee, Zamora hit her with a weight in the forehead before Jones stumbled to a field and into a barbed wire fence, Parrish said.
At that point, he said, Zamora said, "She's not dead. Shoot her, kill her, shoot her."
"David Graham does exactly that," Parrish said. "David Graham puts two bulletsÂ—not one, but two bulletsÂ—in her head."
Parrish also for the first time publicly questioned Graham's claim that he had sex with Jones.
Wendy Bartlett, a schoolmate of Jones, testified Wednesday that she drove Jones home following an out-of-town track meet. It was same night Graham allegedly claimed to Zamora he drove Jones home and had sex with her.
Reported by Angela Hale