The driver of the vehicle was found by deputies inside the vehicle and was able to walk following the crash, Mr. Boyd told KSAT-12.
Images from the scene appeared to show a large four-door SUV-style auto badly wrecked in the middle of the road.
The border agent stopped one of the vehicles and another agent stopped a second one.
Sunday's crash came almost a week after more than 50 immigrants were found inside a refrigerated tractor-trailer Monday in San Antonio.
The third vehicle kept going when agents encountered it, and a sheriff's deputy took over the chase prior to the fatal crash, the border patrol said.
Boyd said the driver and one passenger of the passengers were the only US citizens in the vehicle. Of those five included the driver, who is reportedly a United States citizen.
"We've seen this many, many times and not only in this county but other counties along the border", he said.More news: Tweeple celebrate Mexico’s win against Germany with ‘wall’ memes and jokes
Authorities previously encountered the driver of the SUV last week, and believe he was in the area to pick up or scout unauthorized immigrants, Boyd said. Dimmit County is directly north of Webb County and east of Maverick County, which border Mexico.
Boyd added that a wall is not the only answer.
The Border Patrol says it's providing adequate meals, bathrooms access and medical care to people being held.
Boyd said smuggling endangers not only the lives of Americans but also the lives of the immigrants.
An SUV carrying 14 people rolled over and ejected 12 people who are believed to be illegal immigrants, according to a report from News4SanAntonio.
"It's just extremely busy, we need the assets down here, we have a problem", Boyd said.