RCDs (Residual Current Detectors), which are the EU equivalent to GFCIs, have a trip threshold of 30mA and that is considered "non-lethal" everywhere but North America. We are just beginning to see them here now, but elsewhere in the world, "electric showers" are the norm, which is an instantaneous electric heating element ON the pipe feeding your shower nozzle. Those have to be protected by an RCD and they consider that safe.
Here, 30mA is considered "equipment protection", but our GFCIs (personnel protection) are required to trip at 5mA (at least 4, no more than 6), so 6 times LOWER than what everyone else considers non-lethal. We swim in pools where the electric light is right there with us, hot tubs with electric heating elements right there with us. They are all protected by GFCIs; having a TV on the wall is absolutely no different.
By the way, the risk has absolutely nothing to do with the tub or pipes being metal or not, SOMEWHERE that water is going to make contact with metal that is grounded.
I saw one of the stories about a girl electrocuted "by her cell phone charger" in the bathtub; the detail often left out of that story but mentioned in some versions is that she did NOT use the GFCI protected receptacle in the bathroom, she put her charger on a long extention cord going into another room. The entire end of the cord, WITH the charger, is what fell into the tub with her.