The USB chargers mostly use an electrical design that allows a small percentage of the mains voltage through to charge low voltage devices. Very few of the cheaper systems use a transformer, which would, in theory, completely isolate the mains from the charger output. Instead, a capacitive dropper design is the normal choice for manufacturers, it is cheap, works well but has the disadvantage that one side of the circuitry is connected to the mains. The cheap chargers do not have any form of earth connection, so the output voltage is left floating with respect to earth. Under normal conditions this does not represent a problem.
If you run the back of your fingers along the metal side of a tablet computer or phone while it is plugged in and charging, you will probably feel a little tingle or vibration through your fingers. This is leakage current to earth passing through your body. It is at very low levels, microamps at best and normally completely harmless because your body has a resistance of at least a hundred thousand ohms when dry.
Step into a bath and you reduce the skin resistance dramatically, perhaps to a thousand ohms or less. This allows considerably more current to flow. Add some contaminants such as bath salts to the bath water, and the water conductivity is also vastly increased. Distilled water is effectively an insulator, but add some salt and it readily conducts electricity.
So the floating five volt charger appears pretty harmless, but because the voltage is floating with respect to earth, a much higher voltage can exist between the charger contacts and earth, approximately half of the mains voltage is normal, so 120 volts in the UK.
The next problem is that the mains voltage is not actually 240 volts, that is just the mean value of the sine wave voltage. The peak rises to 315 volts or thereabouts.
So there you are sitting in the bath with a five volt charger, but the actual voltage to earth from either contact is nearly 160 volts. The return earth connection is provided by the copper pipework to the bath. It only takes one milliamp of current to flow across the chest and heart to disrupt the normal heartbeat. An overall resistance of 160,000 ohms is required to limit current to this level. As mentioned earlier, the actual resistance of a body immersed in bath water is probably less than a thousand ohms. This would allow a current of 160 milliamps to flow, easily enough to kill.
Almost certainly, the charger being used in this incident was one of the cheaper after market ones sourced from the Far East, although any device connected to the mains in a bathroom represents a considerable risk to the user unless specifically designed and certified for such use.