Apparently it isn't true, and some studies suggest that it may have a negative effect on your posture.
a 2009 British study found that prolonged sitting on a therapy ball led to just as much slumping and “poor sitting position” as a desk chair.
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The balls produced more muscle activity and 33 percent more “trunk motion.” But they also produced more spinal shrinkage... “It is concluded that the advantages with respect to physical loading of sitting on an exercise ball may not outweigh the disadvantages,” the researchers wrote.
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Other studies have had similar results.
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THE BOTTOM LINE Sitting on an exercise ball burns more energy than sitting on an office chair, but the evidence that it improves posture is lacking.
Source: The New York Times The Claim: Replacing Your Desk Chair With an Exercise Ball can Improve Your Posture. By Anahad O'Connor Published: September 20, 2010