Burke Ramsey Reveals Who He Thinks Killed Sister JonBenét

In the nearly 20 years since JonBenét Ramsey was killed, her brother, Burke, and their parents, John and Patsy Ramsey, have been on the receiving end of continued scrutiny – an "umbrella of suspicion," as it was once described.

While theories abound about who strangled the 6-year-old girl in December 1996 and left her body in the family's Boulder, Colorado, home, Burke is adamant on one point: The Ramseys were not involved.

"It blows my mind. What more evidence do you need that we didn't do it?" Burke, now 29, said Monday of his family's innocence, during the final installment of his three-part Dr. Phil interview, his first public sit-down since the crime.

Earlier in the special, Burke assured of a theoretical cover-up, "You won't find any evidence because that's not what happened."

Patsy, John and Burke – who was 9 at the time of the killing – were never charged in JonBenét's death and have always maintained their innocence.

The local prosecutor later declined to prosecute John and Patsy, following a grand jury proceeding against them, citing a lack of evidence.

Now, John and Burke are the family's only surviving members: Patsy died in 2006 from ovarian cancer. Two years later, then-District Attorney Mary Lacy wrote a letter to John saying that DNA evidence cleared the trio. (A decisive announcement some in law enforcement criticized as premature.)

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Decades later there remains rampant speculation about the role of JonBenét's family in her death – which Dr. Phil McGraw brought up in his special.

But the Ramsey men have their own theories about what happened all those years ago. Burke said on Dr. Phil that it was "probably some pedophile in the pageant audience."

JonBenét performed in child beauty pageants in the time before her death, and Burke speculated in his interview that the culprit "saw her at one of the pageants."

John, now 72, said he believes that it was an intruder who entered the home while the family was out on Christmas Day, 1996, possibly hiding in one of the upstairs bedrooms.

"They came in when we left and were there when we came home," John told McGraw.

As PEOPLE reported in a recent cover story, investigator Lou Smit has said a broken basement window, an unidentified footprint near the body and trace male DNA evidence on the scene proved that an intruder was the perpetrator. Boulder police, however, considered those signs inconclusive, pointing to dust and an undisturbed spider web around the window as evidence that undermined the theory.

"People still can't get that in their head that we didn't do it," Burke told McGraw on Monday, adding that he thinks JonBenét and his mother are "together again," watching over him.

In fact, Burke said that he has talked to JonBenét in the years since her death.

"Like, 'Hey, thanks for looking out for me ... Hope you're having fun up there, because I'm taking some test,' " he explained.

He said said he "keeps the hope alive that [JonBenét's killing] will [be solved in my lifetime]. I don't know, but you gotta never give up."

He said the focus should be on remembering his little sister, a girl who loved ice-skating and the outdoors.

John, meanwhile, said his Dr. Phil interview will be his last with the media, assuring, "I have no intention to speak out ... in the future."

He said, "The real story here is not that a child was murdered. The real story is what was done to us by [the system]."