What is the rear end sag set too? If you have too much preload (not enough sag) it can be very unstable.
I had a 99 KX125 (practically the same bike). It suffered from horrible head shake first ride out. Turns out the previous owner was either huge, or couldn't set up the suspension. My 180 lbs had only a little over 2" of sag (should be roughly 4"). Setting it up helped a huge amount, but it was still fairly unstable. A new front tire basically cured it. The on there was slightly dry rotted and probably had soft sidewalls.
As for the whole steering stabilizer thing, your theory is way off. Just because a bike is geared to do, say, 70 mph, it sure doesn't mean it has the ability go that speed in all situations. If you are doing a lot of high speed riding a stabilizer can be a godsend on any bike. :ride: