Ms. Brown, the education advocate who also investigated segregation academies, estimated that maybe one or two of these private schools had lost their tax-exempt status, despite years of work and multiple reports filed to the federal Department of Health, Education and Welfare. “Nixon was president then, and he wasn’t going to do anything about it,” she said.

Houston Academy maintains its tax-exempt status. Today, its once bare-bones campus has a country-club feel. White columns adorn the front entrance, and the admissions office that Mrs. Clinton would have visited is now decorated with a kaleidoscope of flags of Ivy League schools.

On a recent afternoon, students in uniforms of khaki shorts and blue polo shirts ate lunch in a maze of manicured courtyards with waterfalls. The farmland that once surrounded the school is now an upper-middle-class subdivision.

In 2013, eight of Houston Academy’s 527 students were black, according to the National Center for Education Statistics. The current headmaster, Scott Phillipps, said that nearly 10 percent of the students were minorities, including blacks, Indians, Latinos and Asians, and that the school, which costs around $10,000 a year, offered scholarships and tried to lure students and teachers of diverse backgrounds.

“If you want to narrowly define diversity in terms of African-Americans, that’s kind of Old South,” Dr. Phillipps said. “We’re trying to be global.”

In August 1972, when Mrs. Clinton had completed her research into segregation academies, she joined Mr. Clinton in Austin to help register voters in South Texas. She then returned to New Haven to complete her law degree, and went on to other projects for the Children’s Defense Fund before moving to Arkansas, marrying Mr. Clinton and beginning her legal and political career.

The proliferation of private schools in the South “was a gigantic event, and it blew the minds of civil rights folks and took the wind out of their sails,” said Douglas A. Blackmon, a Pulitzer Prize-winning author at the University of Virginia’s Miller Center who is working on a documentary about the effects of segregation academies.

“But in a minute, it was over,” he said of the effort to combat such schools. “And the well-intentioned work Hillary described was no match for the absolute insistence of millions of Southern whites that their kids never go to school with black kids.”