Which details of Beatty's account of firemen make it credible/incredible? Is his account a history or simply a fable meant to influence Montag's behavior?

Beatty presents real facts about society, which Montag can recognize as true. This makes his speech believable, but he manipulates the information in the speech to influence Montag's behavior.

According to the context of the question, we can see that you are referring to the book "Fahrenheit 451" where we are introduced to a society where books are banned and burned by firefighters.

Montag is one of those firefighters, but after having access to a few books, he begins to question whether his profession acts correctly and whether books, in fact, need to be banned and burned.

Upon realizing this, Captain Beatty, who is the captain of the firehouse to which Montag is a part, gives a long speech, showing why the books were burned and how the firefighters' work began.

Beatty shows that books allowed people to perceive their realities, have ideas, feel sad about situations they cannot change and contend with each other because of different ideas.

He says that the thinking triggered by the books made people unhappy and that was socially disadvantageous. For that reason, the work of firefighters is so important.

Montag recognizes that books are capable of providing questions and interpretations of reality that do not always develop happiness and, therefore, realizes that Beatty's speech is believable.

However Beautty manipulates the information in the speech, without showing that through books society has knowledge and freedom and these are the main basements of happiness. This manipulation is done to influence Montag to behave in favor of firefighters and against books.

You can have more information about this book at the link below:

synonymous.

he was ashamed of himself