“I only tell true stories,” Carly Fiorina assured employees during one of her first speeches as the chief executive of Hewlett-Packard in 2000.

But the stirring story that Mrs. Fiorina, now a Republican candidate for president, told that day about the creation of HP and its first product, had a glaring problem: It was almost entirely inaccurate, according to an internal transcript, an oral history of HP, a book and a company historian.

In the end, it may not matter.

In the 2016 presidential campaign, the truth is starting to look deeply out of fashion.

Donald J. Trump has brazenly denied calling Senator Marco Rubio the “personal senator” of Facebook’s founder, Mark Zuckerberg — even though the quote was published on Mr. Trump’s campaign website.