The arguments are in one of three "friend of the court" briefs filed this month with the 5th U.S. Circuit Court of Appeals, which is considering the lawsuit filed by Sergio Hernandez's parents for the second time Wednesday.
All three briefs ask the court to overturn U.S. District Judge David Briones' ruling that the family cannot sue agent Jesus Mesa Jr. over the shooting in 2010.
A three-judge panel ruled 2-1 on June 30 that the family could sue Mesa. He won a rehearing by the full 15-member court.
According to the lawsuit, Hernandez and other youths were running up a culvert to touch the barbed-wire fence between Mexico and the United States, then running back. Mesa detained one of the friends, Hernandez retreated and Mesa shot him, the lawsuit alleges.
U.S. investigators did not charge Mesa, who reportedly said he was protecting himself against someone throwing rocks.
"Three videos and a U.S. Department of Justice investigation disproved an initial FBI press release that implied that Sergio had thrown a rock at the agent," the Hernandez' attorneys said in a footnote to their arguments, citing an article on the El Paso Times website.
Judge Briones ruled in 2011 that the family could not sue the United States, Mesa or two of his supervisors because Hernandez was in Mexico when he was killed.
The 5th Circuit panel agreed that the federal government was immune from the suit and the supervisors were not involved. However, two of the 5th Circuit judges held that the family could sue Mesa.
"A strict, territorial approach would allow agents to move in and out of constitutional strictures, creating zones of lawlessness," Judge Edward Prado wrote. "That approach would establish a perverse rule that would treat differently two individuals subject to the same conduct merely because one managed to cross into our territory."
The judges based their decision partly on the U.S. Supreme Court's 2008 ruling that foreign terrorism suspects held at Guantanamo Bay have the right to challenge their detention in federal courts.
Briones said that decision doesn't apply because the high court didn't mention the Fourth Amendment right against unreasonable searches and seizures. Prado wrote that although it dealt with one specific bit of the Constitution, "its reasoning was not so narrow" and was about when the U.S. Constitution might apply to events outside the United States.
Mexico's brief says it respects the United States' interpretation of its laws and Constitution, but the U.S. should provide a way to compensate victims and hold its agents accountable if they violate Mexicans' fundamental rights.
"Practicality and common sense — as well as the United States' international human rights obligations — demonstrate that the U.S. Border Patrol's obligation to refrain from unjustified use of deadly force does not vanish when the victim is located just across the border in the territory of a foreign nation," it said.
The other "amicus curiae" briefs were filed by Guinevere E. Moore and Robert T. Moore, who teach constitutional and human rights law at St. Mary's University School of Law in San Antonio, Texas, and by the Border Network For Human Rights, Paso Del Norte Civil Rights Project, and Southern Border Communities Coalition.
Those who file such briefs do not usually participate in oral arguments.
Copyright 2015 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.