“How many others are not scaling up to cure cancer, to help the environment, because there is a belief we shouldn’t invest in those things?” said Mr. Nardizzi, who was given $473,000 in compensation in 2014.

The Wounded Warrior Project’s roots are more humble. Its founder, John Melia, was a Marine veteran who had been injured in a helicopter crash off the coast of Somalia in 1992. When wounded troops began returning from Iraq in 2003, Mr. Melia remembered how he had arrived in a stateside hospital with only his thin hospital gown, and began visiting military hospitals to distribute backpacks stuffed with socks, CD players, toothpaste and other items.

As the backpack project grew, Mr. Melia hired a few employees, including Mr. Nardizzi, a lawyer who had never served in the military but was an executive for a small nonprofit, the United Spinal Association, which served disabled veterans.

They began raising millions of dollars and broadening their services to include adaptive sports for disabled veterans, employment and benefits help, and retreats to teach veterans to cope with post-traumatic stress disorder.

By 2009, the group had grown to about 50 employees and $21 million in revenue. But by then, Mr. Melia and Mr. Nardizzi were fighting over the charity’s future, with Mr. Nardizzi pushing for more aggressive expansion than Mr. Melia, former employees said.

In January 2009, Mr. Melia resigned.

Mr. Nardizzi said in an interview that Mr. Melia left to pursue business ventures. But Mr. Melia’s ex-wife, Julie Melia, who worked at the charity at the time, said in an interview that her former husband felt like the organization was “stolen from him.”

“He didn’t want to leave, but it was obvious something was going to happen,” Ms. Melia said.

The organization paid Mr. Melia at least $230,000 after he stepped down, according to tax forms. He has never spoken publicly about his disagreements with Mr. Nardizzi, and declined to be interviewed.