“You have an obligation to behave in the interest of that organization,” said Linda Sugin, a professor of nonprofit law at Fordham University. “The problem is, when you’re on both sides of the transaction, then we’re skeptical that you’re going to put the organization’s interests before your own.”

Ms. Sugin said the institute could have reduced its risk by soliciting bids from competing firms to gauge whether the insiders were charging market rates. The institute could have asked its leaders to recuse themselves from the decision to hire their own companies, she said.