To Americans alarmed by the loss of control at the US-Mexico border, nothing is more enraging than the murder of an American citizen by a migrant who is in the country unlawfully.

A recent grim example was last month’s killing of Laken Riley, the 22-year-old nursing student who was abducted while jogging at Augusta University in Georgia. The suspect in the case, Jose Antonio Ibarra, entered the United States illegally in 2022 and was apprehended by Border Patrol agents. But he was released on parole, allowing him to remain until his asylum claim could be adjudicated. Over the next 18 months, though he was arrested on various charges in multiple jurisdictions, he was never deported. He is accused of attacking Riley with a blunt object, fatally “disfiguring her skull,” and then attempting to hide her body.

During his State of the Union address on March 7, President Biden mentioned Riley’s death, which has become a cause célèbre among Republicans and immigration hardliners. He said his “heart goes out” to the parents of “Lincoln [sic] Riley, an innocent young woman who was killed by an illegal.” Among some members of Biden’s party, there appeared to be more consternation over his use of the word “illegal” than over the death of the innocent victim.

There have been other cases of tragic deaths caused by migrants who were in the country unlawfully.

In 2016, Sarah Root was killed when a drunk and speeding driver, Eswin Mejia, slammed his truck into her car. Mejia, an illegal immigrant from Honduras, was charged with vehicular homicide, but he made bail and disappeared.

Just days ago, Brandon Ortiz-Vite — a Mexican citizen who twice broke the law to enter the United States — was charged in Grand Rapids, Mich., with carjacking and felony murder for the killing of Ruby Garcia, whose body was dumped on the side of a highway. In February, police in Maryland arrested Nilson Trejo-Granados in connection with the killing of 2-year-old Jeremy Poou Caceres, who was killed in the crossfire of a shootout. The suspect is an undocumented El Salvadoran national with numerous previous arrests. He was repeatedly set free by Montgomery County, Md., authorities, despite several Immigration and Customs Enforcement requests for his detention.

Such tragic episodes are travesties. They make a mockery of the law. They inflame a sense that disarray at the border has become the most critical threat facing the nation. Above all, they are a boon to anti-immigration demagogues who claim falsely that illegal migrants are more likely to commit murder, rape, and other violent crimes than US-born citizens.

I repeat: who claim falsely. Nativists like Donald Trump have long promoted the idea that foreigners who enter the country without lawful documents are “criminal aliens” and pose an abnormally serious peril to public safety.

However popular that belief may be in some circles, it isn’t true.

Researchers have confirmed again and again that immigrants to the United States — authorized and unauthorized alike — are significantly less likely than native-born citizens to commit serious crimes or be in prison. For example, a peer-reviewed 2020 study published by the National Academy of Sciences found that “undocumented immigrants have substantially lower crime rates than native-born citizens and legal immigrants across a range of felony offenses.” Last month, Cato Institute scholar Alex Nowrasteh, who has been studying the connection between immigration and crime for years, released a new paper based on data from Texas, the only state that records the immigration status of people arrested and convicted of various crimes. His calculations established that the homicide conviction rate in Texas is 2.4 per 100,000 among undocumented immigrants — lower than the rate of 2.8 per 100,000 for native‐born citizens.

It should go without saying that statistics on the rarity of violent crime committed by immigrants who crossed the border illegally don’t mitigate the horror suffered by victims like Laken Riley and Ruby Garcia or the pain endured by their loved ones. Violent criminals ought to be arrested, prosecuted, and punished regardless of their immigration status, and convicted offenders who aren’t citizens should be deported. It’s unconscionable that “sanctuary” jurisdictions impede the government’s ability to remove the tiny number of undocumented migrants who are discovered to be dangerous lawbreakers.

It is likewise unconscionable to pretend that the violent crimes committed by an atypical sliver of those immigrants prove that immigrants are making the country less safe. Immigrants tend to be unusually law-abiding. True, there are appalling outliers. But public policy should be based on the rule, not the exceptions. Agitators like Trump and other nativists on the right harp on the exceptions because it advances their long-standing anti-immigrant agenda. Yet one could just as readily point to spectacular acts of goodness performed by unlawful migrants as a reason to throw the gates open.

On the day of the Boston Marathon terror attack, to mention just one notable local example, Carlos Arredondo instinctively ran toward the explosion, laboring without letup to rescue victims from the debris. In a famous photo, he can be seen helping to rush Jeff Bauman to an ambulance. To prevent Bauman, whose legs were shredded, from bleeding to death, Arredondo had the presence of mind to grip a protruding femoral artery and use his fingers to pinch it shut. Bauman might well have died had Arredondo not reached him in time. Arredondo was a Costa Rican native who entered the United States illegally when he was 19 years old.

Does that prove that migrants ought to be admitted without restriction? Of course not. Some undocumented migrants shed blood. Some turn out to be remarkable lifesavers. The vast majority, however, avoid the limelight and do what immigrants have always done — they work hard to improve their lives and care for their families. Overwhelmingly, they stay out of trouble.

Given the chaos at the border, few would deny that America’s immigration policies badly need fixing. But it doesn’t help the cause of reform to focus on the aberrations. Rabble-rousers who exploit tragedies to demonize all undocumented immigrants are only making a difficult situation worse and deserve nothing but contempt.