Andy Warhol died a quarter of a century ago today, on 22 February, 1987. He is in no danger of being forgotten. But what, exactly, is he being remembered for?

To mark today's anniversary, a new 40-minute film called Andy X, directed by Jim Sharman, who made the Rocky Horror Picture Show, is being released online. You can pay to watch, or alternatively Facebook users can use friends as currency, which is clearly a very Warholian idea. At least, it's the kind of idea we instantly label "Warholian", without thinking about what it really has to do with Warhol or his art. This is part of the problem when remembering Andy Warhol.

More problems arise when you actually look at Sharman's film. It's a musical. OK. It is not the first quasi-operatic meditation on Warhol; this has been done before, by John Cale and Lou Reed on their album Songs for Drella. The briefly reunited, antagonistic former leaders of Warhol's "pop group" the Velvet Underground had several advantages when it came to devising a musical homage to Warhol. For one thing they knew him personally, and for another, they were (and are) giants of alternative rock. Any comparisons with Andy X are cruel, so I won't labour them.

Leaving aside the film's artistic quality, what it says, or does not say about Warhol is revealing. Andy X is all about the image of Warhol – an image the makers seem to have received from sources ranging from other films to sensationalist biographies, but not from Warhol's own art or writings, nor the analyses of people who knew him. It is, consequently, another regurgitation of empty Andy, glamorous Andy, fame-obsessed Andy.

The real Andy Warhol, behind this trashy myth, produced some of the starkest and most compelling images in 20th-century art. His car crash paintings, screen tests, and late religious works reinventing the Last Supper are serious, incredibly human and compassionate works. Warhol was a true artist who restlessly experimented, invented, and confronted the realities of the modern world. His laconic literary and speaking style is itself a monument of modern American culture, a voice to set among those of novelists from F Scott Fitzgerald onwards, who have captured the brittle beauties of the American dream.

Warhol deserves to be remembered for his subtle and honest art, but he seems fated to be remembered more as an "icon" – reduced to an emblem of modern cool. "I'll be your mirror", as the Velvet Underground sang. Warhol was a mirror, which has always been one of the great functions of art. In the end, it does not matter how many fictions are spun about him; this simple, reflective truth will always wait at the heart of the myth. When you find it, you will know by the tingling of your spine.