Lost in the debate over Donald J. Trump’s refusal to release his tax returns is the story of where the custom of disclosure comes from — and why it can be so valuable as a measure of character. It’s a tale of presidential tax shenanigans, political scandal and one of the most famous quotations in American history: Richard M. Nixon’s “I am not a crook.”

The story begins in July 1969, when Congress eliminated a provision of the tax code that had allowed a sitting or former president to donate his papers to a public or nonprofit archive in exchange for a very large tax deduction. Congress’s rationale was that a president’s papers already belonged to the public.

In his taxes for 1969, President Nixon indicated that four months before Congress acted, he had donated more than 1,000 boxes of documents to the National Archives. He claimed a deduction of more than $500,000.

The write-off didn’t become public until 1973, when it was mentioned in passing during a lawsuit related to the Watergate break-in. Although the deed formally giving the papers to the National Archives was dated March 27, 1969, it turned out not to have been signed until April 1970, nine months after presidential document donations lost nearly all their tax benefits. (A thorough account of Nixon’s tax dodge is contained in a paper written for the United States Capitol Historical Society by the Northwestern University law professor Joseph J. Thorndyke.)

Had Nixon really beaten the deadline? And had he overstated the papers’ value to generate a personal windfall? ...