I can think of two possible explanations:
- Probably, there was some misunderstanding due to the fact that many of the DX cameras, such as D3000 and D5000 series do not have an internal motor. As a result the 80-200 AF-D lenses will not focus on them. They will still focus on D90, D7000 and D7100 bodies. On the other hand the 70-200 AF-S lenses have a motor in the lens. So that even D3000 and D5000 series cameras can autofocus with them.
- Another reason may be that full-frame cameras (FX) generally have better high-ISO performance. As a result, one can avoid a need for VR on a telephoto lens while hand-holding simply by raising ISO. On the DX the threshold (of poor light) when one no longer can hand-hold the lens while shooting starts earlier.
In the end, I don't think there is a reason to avoid 80-200 on DX. It is a wonderful lens. It is about half the price of 70-200 VR1 and a third of the price of 70-200 VR2. It is great for portraits and sports alike. For birding one will be better of with 300 f4 for roughly the same price (or cheaper).
Side note: the effect of hand-shake is proportional to the lens magnification. To mitigate it one should use twice as fast shutter for double magnification of the lens.