I have heard the same stories and even the camcorder manufacturers themselves recommend turning off the stabiliaztion devices, BUT...
after missing a few shots (when I grabbed my DESTABILIZED camera off of the tripod) - I figured the heck with it.
Quite frankly I've never seen any real problem leaving the stabilization on all the time.
If we KNOW the camera is going to be "nailed down" we do turn stabiliztion off. For wedding work, I'd personally leave it on all the time.
BTW (and this may be important) - the above commentary is based ONLY on Sony Cameras. I have no idea what bad things could happen with other manufacturers.
AND - my suggestions are solely based on viewing thousands of hours of raw footage for high-end corporate clients. I could be wrong.
Apparently on the Canon XL1:
When you have stabilization on, and the camera is on a tripod:
At the very beginning of a pan, the stabilizer will think that you don't want the motion. So it will compensate.
And then your pan will start, and the stabilizer will realize the shot is moving. So it "snaps" into place.
I have no idea if that makes sense to you. Regardless, if the shot looks fine (evaluate it on a good monitor) then it looks fine.
Sounds like Sony may have a better stabilization algorithm. I left it on while doing pans from a tripod with my Z1 and didn't have this kind of issue. Maybe the Canon doesn't know the difference between a fluid pan and a wobbly run-and-gun. If the software were sophisticated enough, it seems like it should know the difference (like a pan might be mostly linear, fluid motion vs. jerky up-and-down and all-around).
Set one of the "P" buttons on the Z1/FX1 to toggle stabilization on/off. Very quick and easy to change on the fly.
I've used my FX1 with Stabilization on for 18 months before I recently tried different settings. Sony's algorithm on these cameras is very good, as far as I'm concerned.
Higher end camcorders Canon GL2 and above have optical stabilzation... that has NO impact on image quality. Electronic stabilzation does soften the image.