Father Richard Heene: "This is a relief, we're going to watch him a lot closer"
The father of a boy thought to have been carried away by a helium balloon before being found at home has repeated denials that the incident was a hoax.
Richard Heene told US TV networks that the disappearance of his son Falcon, six, was not staged. Police say they intend to re-interview the family.
Falcon aroused suspicions by saying on air he had stayed hidden as his parents "said that we did this for a show".
Richard Heene and his wife previously appeared on reality TV show Wife Swap.
TV network ABC described them as a "storm-chasing, science-obsessed family".
Thursday's balloon drama was itself played out on TV, with US networks devoting their airtime to live footage of the balloon over Colorado.
The balloon landed in fields and was surrounded by rescue vehicles after a two-hour flight, prompting a ground search for the missing boy and further fears for his safety.
But Larimer County sheriff Jim Alderden later announced that the boy had been found alive and well in a box in the roof-space of the garage at his family's home.
He said on Friday that his officers had been convinced throughout Thursday that they had been dealing with a genuine situation.
However, he conceded, the boy's comments while being interviewed on TV had "raised some questions".
"We intend to go back and further ask the family to co-operate with our investigation through answering more questions and resolve this issue," he told the Associated Press.
The news that Falcon had been found safe and well delighted both the Heenes and the TV networks.
However, questions over the family's motivation later emerged during a CNN interview.
Mr Heene was asked by an interviewer to ask his son why he had not emerged from his hiding place when he heard his parents calling out his name.
Speaking hesitantly at first, Falcon answered: "You had said that we did this for a show."
In spite of quick denials from his father, speculation that the Heenes had faked the entire incident persisted into Friday, when the family appeared on more US TV talk shows.
Father Richard, wife Mayumi, three sons - Brad, Ryo, Falcon
Family appeared on reality TV show Wife Swap, described as science-obsessed
Father is an amateur scientist and keen "storm chaser"
Home videos posted on YouTube, including three sons performing rap song
And in a bizarre twist, Falcon himself became ill while his father was asked direct questions about whether or not they had staged an elaborate hoax.
During one interview on NBC's Today show, Falcon vomited live on air as Mr Heene sought to explain his son's comments.
He was also heard being ill off camera during an ABC interview while his father answered the same questions.
Mr Heene battled on while his son was being sick, telling his NBC interviewer there was "absolutely" no hoax.
Heene family address reporters outside their home
"Now I'm starting to get a little ticked off," he said. Insisting that he had nothing to sell and no motivation to force his son into the limelight, he asked: "What have I got to gain out of this?"
Pressed on what his son might have meant, Mr Heene struggled for an answer on CNN on Thursday night, saying that his son must have been confused by the family's previous appearance on Wife Swap.
In a later segment of the interview Mr Heene avoided a request to ask Falcon once again what he meant by his comment, and instead rounded on his questioner.
"I'm kind of appalled after all the feelings that I went through, up and down, that you guys are trying to suggest something else," he said.