It is not true. What makes wind actually be wind is that it is moving relative to something else. On earth, that something else may be you, but on a gaseous planet the only "something else" is other parts of the atmosphere. And there is nothing about a fluid body rotating in isolation that will apply a differential force in a way that will cause a wind.
One way to think about this is that you can convert to a rotating coordinate system. Then you have the fictitious centrifugal and Coriolis forces. But the centrifugal forces are constant and Coriolis forces require existing motion. There is no force that can generate a wind.
The most common source of wind on a planet like Neptune with little energy from the sun will be good old convection, resulting from the initial heat of all the matter coalescing (in many cases near the end colliding at high speeds) to form the planet. The rotation will absolutely play a role in how that wind flows. (I just found one article that says the wind of Uranus and Neptune are in a pretty thin layer and may be driven by liquids condensing and evaporating, but that's still convection and the ultimate energy source is still the difference between the interior and exterior temperatures of the planet.)
There actually is a way rotation can generate wind-causing energy in a non-isolated planet (like Neptune), and that's tidal heating. Triton creates a bulge on Neptune (two bulges, really), and, as Neptune rotates under its moon, the bulge essentially kneads the planet, which will generate some heat which will be part of the heat budget in Neptunian weather. So maybe I'm hiding a "Yes" at the end of an answer that led with "No", but I think you were talking about rotation by itself, and I still say that cannot create winds.
