The pilot reported that he and his wife, a helicopter pilot-rated passenger, departed to the north. The passenger stated that she noticed that the carburetor temperature gauge needle was in the yellow arc and asked the pilot if he would like her to add carburetor heat. The pilot said yes, and watched as she reached for the lever. The pilot did not see her move the lever because her hand was blocking his view. He looked away to monitor the helicopter, which was then climbing to clear the treetops. The pilot stated that about a minute later, as the helicopter reached the shoreline, the engine sputtered and quit. The pilot noticed that the mixture control had been pulled out about halfway, to idle cut-off. He lowered the collective and entered an autorotation, landing the float equipped helicopter on the water. The helicopter then nosed over upside-down and sustained substantial damage to the tail boom and cabin. The pilot reported that there were no mechanical failures or malfunctions with the airframe or engine prior to the accident. The mixture and carburetor heat controls are next to each other on the pedestal.