I am accustomed to being called ignorant by readers, sometimes with good reason. But the disdain for my grasp of reality was overwhelming last month when I tried to explain why I thought the best public charter schools were good examples for raising student achievement throughout the country.

Several readers said charters, privately run public schools backed by tax dollars, look good only because they choose the students they admit. Here are sample comments:

“Charters get to follow their own rules and pick their own students.”

“Really interesting how the author glosses over the fact that charters get to pick and choose their students.”

“Charter schools only accept the very best.”

“Charter schools . . ., like private schools, pick and choose which students to take.”

Those were thoughtful people, but they were wrong. Cherry-picking by charters is rare, and usually unlawful. Even teacher union ads skewering charters don’t accuse them of selecting only the students they want.

Charter enrollment issues require some explaining. Nearly all of the 43 states and Washington, D.C. that have charter schools require that random lotteries be used to select students if there is not room for all that apply. Three states, Arizona, Colorado and Wyoming, don’t require lotteries, but even there officials said charters are using either lotteries or other impartial ways of admitting students.

“They can either use a lottery or simply select the next name on the wait list based on the order in which that child got added to the wait list,” said Peter Mason, vice president for communications at the Colorado League of Charter Schools. The Arizona law requires “an equitable selection process such as a lottery.”

Shaelyn Macedonio, spokeswoman for the National Alliance for Public Charter Schools, said Hawaii requires lotteries at start-up charters but not at regular public schools converting to charter status, since they want to guarantee places for all students already attending the school. Texas requires lotteries at state-authorized charters but not district authorized charters.

So it’s wrong to say that charters are allowed to pick whatever students they want. But that’s not to say some of them haven’t skirted those rules.

In 2016, the American Civil Liberties Union of Southern California and the Public Advocates civil rights law firm found that at least 253 of California’s roughly 1,200 charter schools maintained policies that illegally prevented students from enrolling or remaining at their schools.

A school in Hemet, Calif. said that to apply as a sophomore a student “must be earning an ‘A’ or ‘B’ in both Geometry and Biology.” A school in Redlands said “only students who show steady academic progress . . . will be eligible for enrollment.” Within a few months of the report’s publication, more than 100 charter schools contacted the authors to say they were correcting their policies to get off the bad list. A state law passed a year later clarified that charters may not have any policies that prevent or in any way discourage high-needs students from attending. I suspect there are gaps in enforcement in many states, but the rule is you can’t cherry-pick.

Nationally, many charters are allowed to guarantee admission of any siblings of students already admitted. Some are also permitted to weight their lotteries so that low-income students or students in the school’s neighborhood have a better chance of getting in. Many people think charters do better because parents who apply to them are more supportive of their children. Some research contradicts that. The argument continues.

The most powerful influence on who goes to certain charters is not admission rules but the character of each school. Those that set academic standards very high draw more applications from parents who want that. Those that emphasize the arts, or technology, or the education of students with disabilities attract parents who want those features for their children.

Two of the most controversial but successful charter networks are the BASIS schools in Arizona, Louisiana, Texas and Washington, D.C., and the Success Academy schools in New York City. BASIS requires Advanced Placement courses and exams in at least six subjects for high school graduation. Its middle school students must pass comprehensive exams each year to be promoted. Success Academy eighth-graders also must pass comprehensives. Its high-schoolers must pass five external exams, such as Regents, SAT subject tests or AP exams, to graduate.

Critics say such demands restrict enrollment in those two networks to parents and children who can handle the pressure. Other onlookers, including me, say if parents want schools that demanding, they should be allowed to have them. Many of them pay taxes that support charters.

I think charter schools are one of the most beneficial reforms in public education in the last two decades. That is particularly true for charters that have raised achievement rates among low-income students through longer school days and more support for teachers. But I enjoy my discussions with readers who disagree with me about this and other issues. We all want to get at the truth.