Small bubbles can form within the vascular system, blocking the flow of blood and causing tissue death. Worse, bubbles can form in the gill lamellae and block blood flow, occasionally resulting in death by asphyxiation. Stirring up bubbles during a water change doesn't hurt your fish, but it probably doesn't do much for them, either. I've seen this myth mentioned on the list before, but I never responded until now, because it is beginning to be repeated. They react, typically with organics, to form simpler, more stable compounds.
Chloramines are more stable than hypochlorite, so they remain in the water a little longer.
Co. Lamb, J. 1985. Water Quality and its Control. John Wiley and Sons. U.S. Fish and Wildlife Service. Introduction to Fish Health Management.