Migrant workers harvest strawberries at a farm near Oxnard, California. (Joe Klamar/AFP/Getty Images)

A decision from the federal district court in Brownsville, Texas has thrown the U.S. immigration system into chaos. As the Obama administration prepares an appeal in order to carry out its plan to grant legal status to some four million undocumented immigrants, a close look at the opinion by Judge Andrew S. Hanen reveals a few passages that could be misleading.

These might not have much bearing on the legal dispute in court, but they're worth addressing. If a federal judge has these misconceptions about immigration, plenty of ordinary Americans probably do too.

1. Undocumented immigrants don't cause crime

Hanen writes that crime has come along with illegal immigration, causing a problem for the states that sued the administration in the case. "This continual flow of illegal immigration has led and will lead to serious domestic security issues directly affecting their citizenry," he writes. "This influx, for example, is causing the states to experience severe law enforcement problems."

In fact, data from the U.S. Census show that despite the fact that many immigrants are poorly educated young men, they are less likely to find themselves in prison than citizens born in the country, regardless of their national or ethnic origin, as Rubèn Rumbaut of the University of California, Irvine has documented. The more time that immigrants spend in the country, the more likely they are to be convicted and imprisoned, and their children's rates of incarceration are more similar to the native population's, suggesting that with assimilation, immigrants become more likely to commit crimes.

Other scholars who have examined this question over several decades have found similar results. If anything, immigration has likely contributed to a decline in the crime rate.

2. Undocumented immigrants aren't coming across the border in droves

"Illegal aliens move freely across the border, thus allowing -- at a minimum -- 500,000 illegal aliens to enter and stay in the United States each year," Hanen writes. Here, his statistics are simply out of date. That was true during the Clinton administration, but the number of undocumented immigrants living in the United States reached its highest point in 2007, according to the Pew Research Center. The figure declined slightly after that and has since remained constant, at roughly 11.3 million. Most of them have been here for at least ten years.

As evidenced by the number of would-be immigrants the Border Patrol apprehends annually -- more than 400,000 -- there is still movement back and forth across the border, but aliens are hardly crossing it "freely."

3. The government does not purposefully allow people into the country without papers

"In many instances, the Government intentionally allows known illegal aliens to enter and remain in the country," Hanen writes. The judge goes on to describe how after apprehending a migrant, federal authorities will sometimes schedule a hearing instead of immediately deporting them. In that sense, the government does allow illegal immigrants into the country, and if they don't show up for their hearings, they might remain here indefinitely, as Hanen notes.

There wouldn't be a problem with that sentence if Hanen had written "alleged" instead of "known," but of course, you can't always deport someone just because a law enforcement officer believes them to be undocumented. Plenty of U.S. citizens have been forced to prove their citizenship while being detained on suspicion of illegal immigration.

To be sure, the national system of immigration courts, run by the Justice Department, has more cases than it can handle. As of this summer, a typical case took 578 days to close. Those on both sides of the debate would like the courts to dispense with these cases more quickly. Yet it is odd, in an opinion that focuses on whether the Obama administration followed the appropriate procedures in developing immigration policy, that Hanen apparently suggests summary deportation for suspected illegal immigrants.

4. Increasing security at the border probably won't help

"The Court finds that the Government's failure to secure the border has exacerbated illegal immigration into this country," Hanen writes. Both halves of that sentence raise questions. Not only is it unclear what the judge means by "a failure to secure the border," but also, increased security might not reduce the number of undocumented immigrants living in the country.

Since 2000, the federal government has built close to 700 miles of fence along the southern border, noted Homeland Security Secretary Jeh Johnson in a speech last year. He also said that the number of agents, aircraft and remote surveillance systems on the border has doubled, and that the government has also deployed nearly 12,000 underground sensors and eight drones. During that same period, the number of people authorities are apprehending has declined by 71 percent, suggesting that far fewer people are attempting to cross illegally. Perhaps that's because it's become much more difficult to cross without getting caught, although a more likely explanation is that the U.S. economy weakened.

The federal government has made significant efforts to secure the border, at enormous expense -- the Border Patrol's budget has more than tripled since 2000, to nearly $3.5 billion a year. And indeed, the data suggest that the border is relatively secure. Wayne Cornelius of the University of California, San Diego has conducted surveys in Mexico, finding that most migrants describe evading Border Patrol officers as "very difficult." As Cornelius has documented, more migrants are dying at the border, suggesting they're taking more difficult routes to avoid the federal agents.

Yet it is not clear whether that improvement in security has reduced the number of undocumented immigrants living in the United States, whom the states suing the federal government describe as an onerous burden. That's because the improvement in security at the border has likely had an unexpected consequence. To the extent that migrants believe that crossing the border has become harder, they are not only less likely to attempt to cross it heading northward, but they're also less likely to leave the United States, knowing it will be harder for them to come back if they need to. The fact that more undocumented immigrants are settling in the United States, and that the average length of time that they have lived here is increasing, is evidence for that theory.

If so, increasing expenditures on border security may well turn migrant workers into permanent illegal residents, discouraging the kind of "self-deportation" that Republicans such as former Massachusetts Gov. Mitt Romney have argued would be the best solution to the immigration debacle.