The White House never checked out Grant's story with El Paso police, Carillo told the Washington Examiner.
Carillo said that El Paso police would have shared their concerns about Grant's story, had they been consulted.
"Nobody bothered to check with us," Carrillo told the Examiner. "They would have been informed, as I am telling you now, that our detectives reviewed hours of video and his actions did not match his account."
Although Grant travelled to DC, he didn't get his commendation from Trump, who handed it to Grant's mother instead. That's because the Texas man was detained by the Secret Service before the ceremony, ABC News reported, over an open arrest warrant.
In a statement, the Secret Service confirmed that "a White House visitor with an arrest warrant was temporarily detained" on Monday, although they declined to name the person. El Paso police told ABC News that it was Grant, although it's unclear what charges he faces.
Grant's family didn't immediately return a message. The White House also has not responded to the El Paso police department's allegations.
Grant first described his bottle-throwing bravery in an interview with CNN host Chris Cuomo days after the August 3 shooting. Lying in a hospital bed with tubes sprouting from his nose, Grant choked up describing the attack.
"I saw him popping people off," Grant said. "To deter him, I started just chucking bottles. I just started throwing random bottles at him. I'm not a baseball player, so one went this way and one went that way."
But then, Grant said, one bottle got close enough to catch the attention of the alleged shooter, later identified by police as Patrick Crusius, a 21-year-old allegedly inspired by anti-immigrant hatred.
Loading
"That's when he saw me," Grant said. "He just - boom, boom, boom, boom, boom - just started firing off rounds at me."
Grant was hit twice near the rib cage, the El Paso Times reported. His family told said that he spent two days in a coma before waking up at the hospital.
Grant's story was widely shared after Cuomo's piece aired, and he later met Texas Republican Governor Greg Abbott. He was among five El Paso survivors invited to the White House for an event that also honoured six police officers who responded to a mass shooting in Dayton, Ohio.
"We welcome 11 extraordinary American heroes," Trump said to open the ceremony.
Loading
The police spokesman emphasised that Grant hadn't done anything wrong during the attack - he simply hadn't tried to distract the shooter as he claimed. "We are not demeaning his reaction which are of basic human instincts but they amount to an act of self-preservation and nothing above that," Carillo told the paper.
Police did say they were surprised at how widely the video evidence differed from Grant's telling.
"We've never had anything like this happen, never had a victim's report so skewed from what actually happened," said El Paso Sergeant Robert Gomez, according to KVIA.
The Washington Post