He maintained that the body still needed to be fingerprinted before they made an official announcement.
Burton and Stefaniak were in Costa Rica celebrating her birthday.
A body found in Costa Rica has been identified as a Florida woman who went missing while she was on vacation, according to her family.
Police discovered what appeared to be blood in the apartment where Ms Stefaniak stayed, and analysed surveillance video from the apartment complex.
Stefaniak's family and friends, who live in Tampa, did not hear from her after she texted them from her Airbnb rental on the night of November 27 to say the power was going in and out.
In an interview, family friend Greg Zwolinsky talked about the main concerns and questions that the family had about Stefaniak's disappearance.
Her brother, Mario Caicedo, told NBC News that Stefaniak checked in for her flight back to the USA on November 28 but she never boarded the flight. When that final phone call to a friend abruptly ended November 27, friends and family initially chalked it up to bad weather or a broken phone, but Jaime said Stefaniak always traveled with her iPhone, iPad and computer.
Before the news broke, Stefaniak's family and friends held out hope she was still alive.
Burton told CBS News this week that a rainstorm appeared to knock out the power at Stefaniak's Airbnb.
Officials also said a 32-year-old Nicaraguan security guard was being detained in connection with her death after offering conflicting stories to investigators.
"As a effect of this tracking, at midday we found the decomposing body of a person and according to preliminary investigations it's the body of a woman", stated Chief Walter Espinosa of the Costa Rican Judicial Police force.
Stefaniak's co-workers said she was an excellent employee who could get along with anyone. "We checked her email and she did not take an Uber at 5.10am".
Ms Stefaniak was staying at an Airbnb in the San Antonio de Escazu neighbourhood.
Authorities in Costa Rica, he is from Nicaragua and worked as a security guard at the vacation rental property where Stefaniak was staying.
The State Department is working on the case and are awaiting the results of an autopsy. The body was only half-buried in the ground and had been covered with plastic bags. I started sending her birthday messages and no-one had heard from her at all. "She went there the night before and left at 5 a.m.", said Caicedo. Ms Stefaniak had planned to fly back to the USA the following day but never arrived for her flight.
She later communicated with a friend via Facetime and said that she wanted to go out that night but was too exhausted.