No, it is not a myth. Electrical shock can occur and can be lethal. As @Sanpaco has linked, it has been empirically proven by the Mythbusters, while it has been anecdotally proven by various - incidents - in - the - news.
By code, most if not all bathroom tub and shower and pool pipes are electronically grounded.
Yes, movies and tv do exaggerate how that death happens. In film and tv, death by electrocution in water is very violent, boiling the water and the body flailing. In reality, it does not take much to short circuit the heart, and any constant current through muscles will lock them up. Look at taser videos to see how the body would react.
Dropping a live appliance into a bathtub would result in a direct short to ground. Water, while not a perfect conductor, is a good conductor. Salt water is much better, but 120 to 240 mains voltage will breakdown in water and cause a significant short, compared to the amount needed to stop the heart.
This link is a Google Books copy of Electrical Injuries: Engineering, Medical, and Legal Aspects By Robert E. Nabours, Raymond M. Fish, Paul F. Hill, The linked section describes the forensic history of a bathtub electrocution case. The short of it was that a hair dryer, dropped in a bathtub that was electrically isolated from ground, caused the GFI or GFCI not to trip, resulting in more than 5 milliamps to soar through a women, killing her.
Slightly unrelated, but still important, even a 9 Volt battery can kill, in the right conditions. Surface Skin resistance is fairly high, (500KΩ to 2MΩ), but break the skin, or go through the other bodily openings and the salty and high electrolytic content of the inner body will cause you to die from a 9V battery.