The government, since outlawing books, has revised history to show that firemen were always tasked with burning books rather than putting out fires. Since homes are now entirely fireproof, and people have forgotten much of the unrevised past, this is taken at face value; at one point, the fireman's official rulebook is cited:
"Established, 1790, to burn English-influenced books in the Colonies. First Fireman: Benjamin Franklin."
RULE 1. Answer the alarm swiftly.
2. Start the fire swiftly.
3. Burn everything.
4. Report back to firehouse immediately.
5. Stand alert for other alarms.
(Bradbury, Fahrenheit 451, Google Books)
This is nonsense, of course; Franklin was not only a prolific writer of books, but helped to refine and popularize the printing press for fast reproduction of texts. He also founded the first library, allowing the wider spread of books to people who could not afford them. By revising history and using Franklin, a beloved historical figure, the government is now able to point to historical events to prop up their ideas; since history books are not available -- and since most knowledge is disseminated by the government -- there is no way to argue against the government position.
In Part One of Fahrenheit 451, Beatty tells Montag that Benjamin Franklin was the first fireman in U.S. history. Specifically, he says that in 1790, Franklin's job was to "burn English-influenced books in the Colonies." Historically speaking, it is true that Franklin was involved in the establishing the first fire brigade in America: he set up the Union Fire Company in Philadelphia. However, it was not Franklin's job to burn books; in contrast, it was his job to put out fires and to keep the population of the city safe.
So, by inverting the historical truth, Beatty tries to justify the role of the fireman in society because he knows that Montag is having doubts about his occupation. Moreover, by using a well-known and well-respected figure, like Franklin, he legitimizes the practice of book-burning.
In essence, it does not matter that Beatty's version of history is wrong. What really matters is that people believe it and believe that a man of Franklin's stature supported book-burning and censorship, more generally.