CBP considered the proposed curbs "very restrictive," Fisher told The Associated Press.
Under current policy, agents can use deadly force if they have a reasonable belief that their lives or the lives of others are in danger.
"We shouldn't have carve-outs in our policy and say, except for this, except for that," Fisher said. "Just to say that you shouldn't shoot at rock-throwers or vehicles for us, in our environment, was very problematic and could potentially put Border Patrol agents in danger."
CBP has not released the full findings of the Police Executive Research Forum. Fisher's comments are the most publicly detailed about them.
The internal review began last year after 16 members of Congress raised concern about the May 2010 killing of Anastasio Hernandez, an unarmed Mexican who died from stun gun wounds at San Diego's San Ysidro port of entry. Authorities have said he was being combative while being returned to Mexico. The Justice Department is investigating that killing.
Hernandez was one of 20 people killed by CBP officials since 2010, including eight who died in rock-throwing incidents with Border Patrol agents, according to the American Civil Liberties Union.
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