In his letter to fans on Wednesday, Washington Redskins owner Dan Snyder invoked the name of the Red Cloud Athletic Fund to defend his NFL team’s name, recounting how legendary coach George Allen consulted with the fund, located on the Pine Ridge Indian Reservation in South Dakota, to design the Redskins emblem.

On Friday, officials at the Red Cloud Indian School in South Dakota — the primary beneficiary of the athletic fund — raised questions about Snyder’s account and denounced the team’s name.

“As an organization, Red Cloud Indian School has never — and will never — endorse the use of the name ‘Redskins,’ ” Robert Brave Heart, the group’s executive vice president, and George Winzenburg, the president, said in a statement. “Like many Native American organizations across the country, members of our staff and extended community find the name offensive.”

Allen became involved with the Pine Ridge reservation in the 1960s, when he was an assistant coach for the Chicago Bears, said a Redskins source who was close to Allen but spoke on the condition of anonymity because of the sensitive nature of the situation. Allen — the father of Redskins General Manager Bruce Allen — did not do it for “politically correct reasons,” the source said, but because he wanted to help.

George Allen started the Red Cloud Athletic Fund with professional baseball pitcher Paul “Dizzy” Trout and others, according to Red Cloud school officials. The fund was based in Illinois but raised money for athletic equipment and facilities for Red Cloud students. It appears to have stopped operating after 2000, the last year it filed a 990 tax return.

Through the fund, the coach developed personal relationships with Pine Ridge residents, the source said. And for his efforts to help the school, Allen was given a plaque that still hangs in the Redskins’ headquarters and that Snyder refers to in his letter to fans. The inscription on the back reads: “This Indian Prayer plaque has been especially made by the Sioux Indian people of the Pine Ridge Reservation for George in appreciation of the kind and generous help given to Sioux Indian children of the Red Cloud Indian School.”

The fund, said Brave Heart and Winzenburg, “was a generous, independent entity that worked to support athletics at Red Cloud Indian School at one time and benefited hundreds of our students.” However, he said “the Red Cloud Indian School was not involved in conversations around an emblem for the Washington Redskins football team.”

In his letter to fans, Snyder cited the athletic fund’s help in designing the emblem, along with the plaque given to Allen, as one of several examples of Native American support for the team’s name. The coach, who died in 1990, often told the story of how he consulted with Pine Ridge friends about changing the emblem, said the source who knew Allen.

Red Cloud Indian School officials said that it was possible Allen dealt with people whom he personally knew on the reservation, but that, as far as they know, the school played no part in it.

“There is no way for me or [the school] to corroborate or dispute that claim,” Brave Heart said. “My concern is that readers may be inclined to believe that Red Cloud Indian School endorsed the use of the Redskins logo and mascot, when that is completely false.”

One Indian leader did embrace the Redskins name and loved the emblem. Blackfoot tribal leader Walter Wetzel, who was president of the National Congress of American Indians in the 1960s, went to the Redskins decades ago with photos of Indians in full headdress.

“I said, ‘I’d like to see an Indian on your helmets,’ ” which then sported a big “R” as the team logo, Wetzel, then 86, told Washington Post columnist Marc Fisher in 2002. When the team unveiled its new logo featuring the profile of an Indian, Wetzel said, “It made us all so proud to have an Indian on a big-time team. . . . It’s only a small group of radicals who oppose those names. Indians are proud of Indians.”

Wetzel, who lived in Montana, died in 2003. It isn’t clear if he had any involvement in the Red Cloud Athletic Fund, which benefited the Lakota branch of the Sioux Nation, not the Blackfoot.

The Red Cloud school officials described their mission as protecting Lakota heritage, culture and language through its K-12 curriculum.

“We stand against any abuse or appropriation of Native history, culture or heritage — and we believe the use of the name ‘Redskins’ falls into that category,” Brave Heart and Winzenburg said.

Snyder and the football team have been under growing pressure from Native American groups and sports columnists to change the name. President Obama added his voice to the long-running debate this month when he said in an interview with the Associated Press that if he were the owner, “and I knew that there was a name of my team — even if it had a storied history — that was offending a sizable group of people, I’d think about changing it.”

Last week, National Football League officials agreed to meet with the Oneida Indian Nation, which has been campaigning against the name by running radio ads in every city the team plays in this season.

In his letter to fans Wednesday, Snyder rejected any negative characterization of the name. He cited a nine-year-old Annenberg Public Policy Center poll of 800 Native Americans across 48 states that showed nine out of 10 did not find the name offensive. He also quoted leaders of American Indian tribes in Virginia who have publicly expressed support for the name in news stories.