Surely, alot of "unwearable" timepieces are in dire need of servicing, but many people report problems with watches that are new and not in need of servicing.
I have personally observed how twisting a running mechanical movement back and forth AT JUST THE RIGHT FREQUENCY can, inded, bring its balance wheel to a stop. If the watch's mainspring was nearly rundown, this could then permanently halt the motion of the balance wheel until the mainspring was wound again.
Of course, this type of motion would not ordinarily happen on a person's wrist, but there can be other subtle motions of the watch movement caused by such things a one's pulse and any unconscious and generally unnoticeable tremors in the muscles of the arm that might affect a timepiece. However, these motions would certainly not cause the timepiece to stop completely if the mainspring was fully or nearly fully wound, but would only interfer with its accuracy.
As far as Uri Geller is concerned, I have studied much about him and am convinced that he has some unique powers. True, he is / was a showman and, on a few occasions, has "cheated" a bit when he was having trouble using his powers to perform paranormal feats and was under pressure by the media to do so.
However, he was tested at Stanford University during the '80's by a group of physicists under conditions that would have absolutely precluded any fakery and he was able to do some VERY remarkable things such as grasping the end of a Geiger counter probe and by concentrating intently managing to make its radiation counting soar far above the background level.
He was carefully searched before and after such demonstrations to preclude the possibility that he had any hidden sources of radiation on him. He's even performed metal bending demonstrations in which he was provided with carefully marked pieces of various metals by scientists and, by merely stroking them with a finger, made them slowly curl up. There was no fraud involved and several scientific papers were written to describe what he did which the scientists dubbed "The Geller Effects".