He also dismisses the assertion by an investigator hired by the 4-year-old British girl's parents that he knows who took Maddie and how, and where her abductor is now.
He went on to say he believes Maddie is dead, and it doesn't appear her parents were involved in the crime.
She disappeared at a Portuguese resort almost seven months ago when her parents left her alone in the family's suite while they ate dinner out.
48 Hours Mystery spent months probing the case, going undercover in Portugal, in search of the truth.
In a world exclusive, the show talked to a potential key witness.
Jane Tanner told the program, "As I was walking up the road, this man ... was walking across the top of the road, carrying a small child. And the thing that I noticed the most was he was holding her, and I could see her bare feet . . . and the bottom of the pajamas. ... It was just complete shock and complete horror that, you know, I might have seen Madeline being abducted."
After months of reported "Maddie" sightings, Francisco Marco, a Spanish investigator hired by a supporter of the McCanns, is asserting, "We're 100 percent sure that she is alive. ... I know the kidnapper and we know where he is. We know who he is. And we know how he has done it."
When pressed, Marco claimed he couldn't say any more while working the case.
Maddie' mother, Kate McCann, insists, "I strongly believe that Madeleine is out there."
But Joseph Moura, the private eye hired by 48 Hours Mystery says he disregards the claims from both Tanner and Marco.
On The Early Show Monday, Moura told co-anchor Hannah Storm he doesn't believe Marco, and described Marco's statements as "pretty ridiculous."
A member of the public claims to have seen Maddy two days after her abduction in central Portugal, in a van with a man and woman and, perhaps, another man.
Moura was also having none of that, saying it wasn't likely.
"The police had 160 police officers working on this case. If this was a set of facts consistent with the real case, they would have identified this person by now," Moura said.
But he indicated he doesn't feel Maddie's parents were involved in her disappearance.
"Having worked the case and been there to identify a timeline, which was the real important part of this case, the timeline -- was there a window of opportunity for these people to have committed some type of crime and then dispose of the body? We find that the timeline doesn't fit.
"They couldn't possibly have been involved, whether it was accidental or not, they would have had to dispose of the body and there just wasn't enough time."
Moura noted that Maddie's parents were out to dinner five nights in a row with the same people, saying, "They had set a pattern. Every night was 8:30 sharp that they had reservations at the restaurant, and they all went there to dinner, they had between six and seven bottles of wine, they had their dinner. So, when you start looking at that time element, looking at the waiters who served them, looking at the bartenders who brought them the bottles of wine, that's how you set up that timeframe we were talking about."
The McCanns weren't the only ones who left their kids alone at the resort at night, Moura pointed out -- all the people they dined with did, even though a babysitting service was available.
He sat at the same restaurant table the McCanns were at the night Maddie vanished, and their room isn't visible form there, Moura said, noting, "They had no visuals whatsoever."
Moura didn't think Kate McCann refusing to take a lie detector test mattered much. "I think a lie detector test is inconclusive," he said. "I wouldn't take one. I would never advise my client to take one. So, that doesn't necessarily bother me."
As for Jane Tanner, Moura told Storm she "gives a very inconsistent story. It's not a truthful story, and I'm not quite sure why she did it. I mean, the fact is that it would be impossible for all these people to be getting up, going to check on the children, going out for walks, when they had an hour-and-20-minute timeframe. They had their dinner, they had seven bottles of wine, they had their coffees. There's just not enough time to do all these things. She never left their table that night."