But they believed her fib and tried her out -- and were blown away, giving her the starring role in the low-budget Beasts of the Southern Wild over 4,000 other hopefuls.
And now she could become the youngest ever winner of the Best Actress Oscar, at the 85th Academy Awards, the climax of Hollywood's annual awards season, next weekend.
"It was very clear ...you don't meet six-year-olds who have that quality," said director Benh Zeitlin, recalling her audition. "She just had this natural charisma and focus and fierceness and wiseness and morality.
"Coming out of a body that small and a mind that young, it's almost alien and alien in a way that goes kind of straight at your heart .. It's her perspective that unlocks the truth in the film."
That charisma is obvious when you see Wallis being interviewed to promote the movie over recent months, even before it was elevated to the stratosphere by being nominated for four Oscars in January, including Best Picture.
"I was in my bedroom half asleep," Wallis told Jay Leno, about waking last month to learn she was nominated alongside Jessica Chastain, Jennifer Lawrence, Naomi Watts and Emmanuelle Riva, the oldest ever Best Actress nominee, at 85.
"So nothing reacted on the outside, but I was like flipping cartwheels and stuff on the inside," she told the talk show host, whom she admonished -- cutely -- for asking her a question more appropriate for the director.
In the movie Wallis plays Hushpuppy, living in the Louisiana bayou with her hot-tempered and ailing father Wink, in a community threatened by floods driven by melting ice-caps.
Beasts of the Southern Wild won the prestigious Camera d'Or at last year's Cannes Film Festival in France, and the Grand Jury Prize for a dramatic film at Sundance.
The movie's setting was close to Wallis' home: the actress -- her first name is pronounced Qua-ven-zhah-nay -- was born in Houma, Louisiana, on August 28, 2003. The "zhane" part of her name means fairy in Swahili.
Beasts of the Southern Wild was her first acting job, and she only got it after ignoring the filmmaker's audition rules -- perhaps, appropriately, like the character she was asked to play.
"It was for a six-to-nine-year-old. So my Mom said I couldn't go 'cause I was only five. But we just went and we act like we're having nothin' to do; we had done nothin' wrong," she said.
"The character who is Hushpuppy, she does what is right and she is fearless and that's what I did at the audition."
Wallis is the youngest Best Actress Oscar nominee by four years: the next is Keisha Castle-Hughes, who was 13 when nominated for Whale Rider in 2003. The third, Lawrence, nominated again this year, was first tapped in 2010 at age 20 for Winter's Bone.
The youngest ever best actress Oscar winner is Marlee Matlin, who took the prize in 1986 for Children of a Lesser God at the positively mature age of 21 years and 218 days.
The youngest person to ever win an Oscar in any competitive category is Tatum O'Neal, who was just 10 when she took home the best supporting actress prize in 1973.
Wallis is already on her third film -- Twelve Years a Slave, with Brad Pitt, Benedict Cumberbatch and Michael Fassbender, due out in September. She has also made Boneshaker, a short about an African family lost in America.
Whether she wins an Oscar on Sunday or not -- the favorites are Chastain and Lawrence, admittedly -- she is clearly a force to be reckoned with, and an actress to watch out for in years to come.