Image Stabilisation and Clarity

How often do you consider turning your image stabilisation function off to get better image clarity?
Most would answer "never", and to be honest I have always been a bit skeptical of its benefit.  I have read that you should always turn the image stabilisation off when the camera is tripod mounted but have never seen any evidence to prove it worth the effort. However, I was recently shooting landscapes on a tripod using extended shutter speeds (to get a nice smooth-looking sea surface) and could not get a sharp result. I tried one test frame with the IS off and noticed a marked improvement in the clarity of the file.

Itsukushima shrine
Canon EOS 5D MkIII +EF70-200mm f2.8 USM II lens, 30 secs @ F32, ISO 100 with the lens stabilisation turned On.
The resulting file is noticeably spongy...

Exactly the same exposure and treatment - but with the IS turned off.
You can see a huge improvement in image clarity.
Though this was a one-off experiment, the ONLY files that were sharp were the ones without the image stabilisation ON.
From now on, all my tripod work will be shot without the benefit of stabilisation...