“Citizen Kane” was fictiona, but everyone knew it was supposed to be about William Randolph Hearst. “All the King’s Men” was fiction, but everyone knew WIlly Stark was supposed to be Huey Long.
What other thinly disguised biographies are there?
“Primary Colors” about Bill Clinton.
Not a biography, but Inherit the Wind is about the Scopes “Monkey” Trial.
Oops, I misunderstood the OP. Sorry about that.
Never mind.
Edward G. Robinson’s character in Silver Dollar was based on Colorado’s “Silver King”, Horace A.W. Tabor.
Alan Ladd’s character in The Carpetbaggers was based on Howard Hughes.
The OP is looking for movies that claim to be fiction but are actually based on real people; I’d name Psycho, The Texas Chainsaw Massacre, and Silence of the Lambs, all of which are (loosely) based on Ed Gein.
In the opposite direction are films that present themselves as “true stories” but actually monkey around with details to make better art. In that vein would be Amadeus, The People vs. Larry Flynt, JFK, The Doors, Nixon, and pretty much anything else by Milos Forman or Oliver Stone.
Oh, and Fargo. And Schindler’s List.
Woody Allen’s Sweet and Lowdown is about a guitarist who is the best in the world… except for Django Reinhardt. In reality, the lead character is based on Django. A lot of Woody’s other movies pretend to be fictional but borrow heavily from his life. Not that he’s a little self-absorbed or anything. 
Terrence Malick’s *Badlands starring Martin Sheen and Sissy Spaceck is a dramatization of the Starkweather-Fugate killing spree of the 1950’s with different characters and events. Great movie.
The Fountainhead (novel and film) are very very loosely based on Frank Lloyd Wright and WR Hearst.
Interestingly, if you combine the novel Fountainhead with the films Citizen Kane and RKO 182 (which is a more-or-less straight dramatization of Hearst vs. Orson Wells over the making of Citizen Kane) you get a pretty clear, albeit dramatized, picture of Hearst.
While she’s not the title character, Sister Sharon Falconer in Elmer Gantry is based on Aimiee Semple McPherson/
*Bombshell (1933), starring Jean Harlow, is loosely based on the life of Clara Bow, with bits ‘o’ Harlow thrown in as well.
Fanny Brice sued the producers of Rose of Washington Square (1939), because it was so obviously lifted from her life.
Charlie Chaplin’s character in “The Great Dictator” was based on Adolf Hitler.
Sunset Boulevard seems to be based on the life and times of Michael Jackson. Even more strange, since it was made years before Mike made it big with someone little.
Scorsese’s New York, New York uses incidents from Doris Day’s biography.
Then there’s The Greek Tycoon, though, of course, any resemblance is coincidental.
Postcards From The Edge, from the novel by Carrie Fisher, is somewhat autobiographical.
If I recall correctly, that character is based on Eddie Lang, the noted jazz guitarist of the early 1930’s.
The Greek Tycoon (Aristotle Onassis)
The Big Fix (Abbie Hoffman)
Washington Behind Closed Doors (TV movie based on John Dean)
I’d have to know a little more about Lang. We discussed the movie recently in a Jazz Guitar class I’m taking and were told it’s Django. IMDb notes that Sean Penn’s character plays the same unusual kind of guitar Django did.
Wasn’t The Rose (with Bette Midler) rather loosely based on the life of Janis Joplin?