Marla Olmstead made her first abstract painting while still in diapers, crouching on her parents' dining room table. She was not yet 2.

Her big break came when she was 3 and a family friend hung her paintings in a coffee shop in her hometown of Binghamton, N.Y.

By the time she was 4, she was scarfing down cookies at the packed opening of her first solo gallery show. A local reporter covered the story, and The New York Times picked it up.

Within months, this "pint-sized Pollock" had sold more than $300,000 worth of paintings. And then, just short of her 5th birthday, the bubble burst. In February 2005, 60 Minutes aired a report implying that Marla's father, a night-shift manager at a Frito-Lay plant and an amateur painter himself, was guiding her compositions. Sales of the paintings quickly dried up. In his new documentary, My Kid Could Paint That, director Amir Bar-Lev traces Marla's sensational rise and fall, focusing on the media feeding frenzy and on the Olmsteads' efforts to prove that Marla created her paintings unaided.

The film makes for a fascinating story about stage parents, media hype and the ethics of documentary filmmaking. But it gives short shrift to some of the more intriguing questions about what it means to look at a 4-year-old's splattery canvases in the context of art.

Does it matter that Marla has no knowledge of these artistic precedents and, most likely, no clear concept of "art" itself? Can a work of art transcend the intentions of its maker? If a child can make great abstract paintings, does this mean modern art is itself a hoax, a high-culture con game?

Ten years ago, I traveled around Thailand with two conceptual artists, teaching domesticated elephants to hold brushes in their trunks and apply paint to canvas. The project was cheerfully satirical, but the elephants really did learn to paint, and their bold, gestural abstractions were strikingly similar to Marla's.

When people look at abstract paintings and say, "My kid could do that," they're right – up to a point. Given the right materials and a little bit of coaching, any kid – or elephant or chimpanzee – can produce something that looks like art, or at least something that looks like abstract expressionism.

In the 1950s, artists like Willem de Kooning and Jackson Pollock proposed a radically new way of thinking about painting: as the direct trace of the artist's physical engagement with the materials. Harold Rosenberg, the critic who first coined the term "action painting," put it like this: "At a certain moment the canvas began to appear to one American painter after another as an arena in which to act – rather than as a space in which to reproduce, redesign, analyze or 'express' an object, actual or imagined. What was to go on the canvas was not a picture but an event."

The Ab-Exers were great formal innovators, but even more important than Mr. Pollock's drips or Mr. de Kooning's arabesques was their revolutionary insight that a painting can represent nothing other than the process of its own creation.

Now, more than half a century later, we're still reeling from this revelation. Hence the continuing fascination with cases like Marla's. For those who believe that painting must be about something more than just color and gesture – like craft or technical skill or mimetic representation – abstract paintings by children and animals provide the ultimate refutation, proof that modern art is indeed a hoax.

But such skeptics profoundly miss the point of the art they're trying to debunk. Yes, anyone can pick up a brush and slather paint on canvas in a drippy style that evokes Jackson Pollock. But it took an artist like Mr. Pollock to step back from his own work, which at the time looked unlike anything that had come before, and say, with bold conviction: "This is it. This is what modern painting looks like." He taught us how to see art in a new way.

Marla and the elephants may be terrific painters – but they're not artists. Art is not just about making things or slapping pigment on canvas; it's also a way of thinking and seeing.

But this doesn't mean we should dismiss them entirely. As viewers, we can appreciate their paintings as art, even if they didn't intend them as such. And, as the stars of their own media circuses, these exuberant painters serve a crucial role as catalysts for discussion, inadvertently prodding a broader public to come to terms with the midcentury revolution in seeing that permanently and profoundly changed modern art.

Mia Fineman is a writer and curator in New York.

My Kid Could Paint That opens Nov. 2 at the Angelika theaters in Dallas and Plano. It's rated PG-13.