Police asked Patsy Ramsey if she would meet with John Mark Karr

As questions mounted on Friday about John Mark Karr’s alleged admission that he killed JonBenet Ramsey in 1996, it emerged that the little girl’s mother, Patsy Ramsey, almost met Karr before her death from cancer in June.

As they pursued their investigation, authorities asked Patsy in late May if she would be willing to meet Karr, the Ramsey family’s attorney, Lin Wood, told the Associated Press. Patsy agreed to meet him if it would help the case, but she died before any such meeting could take place, said Wood.

Karr, a 41-year-old former schoolteacher, was arrested in Thailand on Wednesday and allegedly confessed to the murder, one of the most high-profile unsolved mysteries of recent times. But certain aspects of his story already appear to be unraveling, and the confusion only deepened on Friday, as Thai authorities changed some details of their account of what Karr told them.

Speaking with the AP, Lt. Gen. Suwat Tumrongsiskul originally said Karr told him that he’d sexually assaulted JonBenet and given her drugs. Suwat also told a press conference Thursday that Karr said he had picked up Ramsey at school. On Friday, however, Suwat confirmed to the AP only the sexual-assault confession. He could not confirm that Karr said he had given the girl drugs, and Suwat admitted that the story about Ramsey being picked up from school came from a documentary he had seen and not the interrogation.

At a press conference in Bangkok Thursday, Karr said, “I was with JonBenet when she died.” Visibly nervous and stuttering as he spoke, Karr added, “Her death was an accident. I loved JonBenet.”

However, Karr’s ex-wife, Lara Knutson, who was 16 when she married Karr, told KGO-TV in San Francisco that she was with Karr in Alabama the entire Christmas season when JonBenet was killed. The 6-year-old girl was found beaten and strangled in the basement of the family’s home in Boulder, Colo., on Dec. 26, 1996.

To back up her claim, Knutson is now searching for evidence that will prove Karr could not have killed Ramsey, Knutson’s attorney, Michael Rains, tells PEOPLE.

“She’s got homework to do,” he said. “She’s going to go through old records, photographs, home movies – anything she has from that time period to show that Karr was with his family in Alabama that Christmas.”

Karr’s brother, Nate, has also brought John Mark Karr’s comments into question, telling Atlanta FOX affiliate WAGA that his family will provide information to prove the allegation that Karr killed Ramsey is “just ridiculous.”

Karr’s arrest in Bangkok came about after University of Colorado professor Michael Tracey’s contacted authorities in Boulder. Tracey, who produced a documentary about the JonBenet killing, had been communicating with Karr for at least two years, said university spokesman Barrie Hartman.

For now, Karr continues to be held in a Bangkok immigration detention center. He is expected to be brought to the U.S. as early as this weekend.

Boulder, Colo., authorities are keeping mum about the investigation. District Attorney Mary Lacy said Thursday, “John Karr is presumed innocent,” investigators have “much more work” to do, and the public should not to rush to judgment.