CBS News correspondent Don Teague reported police dash cam video shows the Hartleys pulled over shortly before they went to Falcon Lake in Texas, which supports her story and timeline.
Mexican authorities initially questioned Tiffany Hartley's story, but Zapata County Sheriff Sigifredo Gonzalez, who is investigating the shooting, says he has no doubt she's telling the truth.
Gonzalez said, "There's no reason for us to doubt what she's saying. Our investigation is really for us to get a body."
Teague added Mexico announced on Friday it's launched a formal investigation into the alleged shooting on Falcon Lake.
Authorities there are also ramping up the search for Hartley's body with boats, soldiers and a military helicopter.
Eduardo Arnal, of the Consul General of Mexico, told CBS News, "I can assure them that the Mexican government will do anything in its hands in order to find David and to find what happened in this case."