Police say no campsite was found at the nature reserve during search for Brian Laundrie

(CNN) North Port Police say investigators did not find a campsite in the sprawling nature reserve that has been the focus of the search for Brian Laundrie, the missing fiancé of Gabby Petito.

Police spokesperson Josh Taylor's confirmation that there was no campsite comes after a source close to the Laundrie family told CNN's Chris Cuomo that they had been informed by investigators that police had made a discovery in Florida's Carlton Reserve.

The source on Thursday insisted that the Laundrie family had been told a campsite had been found.

"Is it possible that they thought that there might be a campsite out there or something they may have seen from the air but when they got on the ground that's not what it turned out to be? Sure, I think that's a possibility," Taylor said. "Bottom line, is that investigators are telling me that no campsite was found out there."

Also on Thursday, Laundrie's father, Chris Laundrie, visited the reserve, a 24,565-acre wilderness near Laundrie's family home, for several hours to help in the search, family attorney Steven Bertolino told CNN. The father showed police the trails and locations where he and Laundrie have hiked and frequented, Bertolino said.

"There were no discoveries but the effort was helpful to all," Bertolino said. "It seems the water in the Preserve is receding and certain areas are more accessible to search. The entire Laundrie family is grateful for the hard work of the dedicated members of law enforcement that have been searching the Preserve for Brian over the last few weeks. Hopefully Brian will be located soon."

Her remains were recovered September 19 in Wyoming, near where the couple had last been seen together, and a coroner determined she died by homicide, the FBI said.

In recent days, investigators have uncovered new details about Laundrie's earlier movements at the reserve.

North Port police confirmed that a notice was placed on an abandoned Ford Mustang belonging to the Laundrie family outside the Myakkahatchee Creek Environmental Park on September 14. The park acts as an entrance to Carlton Reserve.

Bertolino, the family attorney, told CNN that upon further communication with the FBI, "we now believe the day Brian left to hike in the preserve was Monday September 13." His parents had previously told authorities he had left on September 14.

Chris Laundrie went to look for his son on the night of September 13 when he didn't return from the park, Bertolino told CNN on Wednesday.

The next day, Brian's parents returned to the area to look for Brian and saw the citation on the car, Bertolino said. The parents returned again the next day, September 15, to retrieve the vehicle.

"The Laundries were basing the date Brian left on their recollection of certain events. Upon further communication with the FBI and confirmation of the Mustang being at the Laundrie residence on Wednesday September 15, we now believe the day Brian left to hike in the preserve was Monday September 13," Bertolino said.

CNN asked Bertolino whether Brian's parents believe he's in the reserve or another area. "No, they don't believe he's in another area. They believe he is in the preserve," he said.

'I want to see him in a jail cell for the rest of his life'

Petito's body was found about a five-to-10-minute walk from where her van was last seen near the entrance to the Grand Tetons, on the border of Bridger-Teton National Forest, according to her mother Nichole Schmidt and stepfather Jim Schmidt during the second installment of an exclusive interview with the "Dr. Phil" show that aired Wednesday.

Gabby's body was in a clearing and was just in front of the remnants of a fire ring, Jim Schmidt said. "You could see where the rocks had been moved to make the fire ring," he said.

"It's definitely not an area that was heavily trafficked," he added.

Jim Schmidt left a memorial and sunflowers at the site, CNN has previously reported.

The Schmidts were joined by Gabby's father, Joe Petito, and his wife Tara Petito, along with their attorney Richard Stafford, for the interview with host Phil McGraw.

Joe Petito said he wants Laundrie found alive so he can spend his life behind bars.

"I want to see him in a jail cell for the rest of his life where -- he's an outdoorsman -- being in that concrete cell and he can't go see those trees and hug -- and smell the fresh air like that," Petito said.

"I want to look him in the eyes," Nichole Schmidt said.

Bertolino declined to comment Wednesday on the "Dr. Phil" interview.

In late September, Laundrie's parents released a statement through their attorney, saying, "Chris and Roberta Laundrie do not know where Brian is. They are concerned about Brian and hope the FBI can locate him. The speculation by the public and some in the press that the parents assisted Brian in leaving the family home or in avoiding arrest on a warrant that was issued after Brian had already been missing for several days is just wrong."