Officials said later that there were no grounds for criminal charges against the family, and that the family would not be charged for the cost of the search.
However, when the family subsequently appeared on CNN's "Larry King Live" via remote hookup, guest host Wolf Blitzer asked why Falcon did not come out of hiding earlier as his name was called. After the boy's father relayed the question, Falcon said, without further elaboration, "You guys said that we did this for a show."
Later, toward the end of a lengthy interview, Blitzer asked Richard Heene to ask his son, who could not hear Blitzer, what he meant by the comment. Heene briefly suggested Falcon might have been talking about the family's two appearances on the ABC show, "Wife Swap."
Heene and his family's appearances on other local and national media outlets also were collected on a Web site, http://www.thepsyiencedetectives.com/, until the site stopped loading while authorities chased the balloon across the skies of Colorado.
As Heene continued to field Blitzer's question about Falcon's quote and was asked to respond to suggestions the incident could have been a publicity stunt, he appeared to grow more indignant.
"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 finally said.
The 20-foot-long, dome-shaped aircraft covered with foil was built by Richard Heene, a former weatherman who said he was designing an aircraft for commuter travel.
"We were working on an experimental craft -- I call it the 3D LAV, a low-altitude vehicle for people to pull out of their garage and hover above traffic for about 50 to 100 feet," Heene said later. "It's still the very early stages of the invention."
The Federal Aviation Administration and Army National Guard tracked the balloon before it returned to the ground. The Army National Guard said it sent a helicopter to monitor the aircraft, and the Colorado National Guard sent up a Kiowa UH-58 helicopter, "deployed to locate the balloon."
ABC News' Clayton Sandell in Denver contributed to this report.