Does a dangling wire really electrocute me if I'm standing in water?
Oh yes.  The phenomenon is called "Electrical Drowning".

In this tragic case, a girl decided to dance in a fountain, unawares that the underwater lights had a ground fault. Her muscles contracted and she fell down. One friend went in to try to grab her, and she too lost control of her leg muscles and fell down. Her two other friends tried to rescue the first two.

Firefighters showed up, one tiptoed in, lost it and his friends yanked him out. The firefighters spent 15 minutes trying to find the shutoff switch.

The problem with falling down in water is that you drown. All four girls did.

In fact, multiple victims is often the only clue to an electrical drowning.

This is why any beachside installations now require GFCI and shutoff switches, and why you should not swim near a boat on shore power.

Why electrical drownings happen

You've seen problems involving grids of resistors. That's what water is, a 3-D grid of resistors, and you also are some of the resistors.

Electrical current travels all available paths in proportion to their conductance (1/resistance). 1-10&nbsp;mA is enough to start causing problems for a sensitive person; 100&nbsp;mA is lethal in its own right.

Electricity wants to get back to source (the pole transformer's neutral), and the NEC standard for a grounding rod is 25 ohms. You can do the math here.

Well, I get 120 V through a 24 ohm resistor = 5 amperes. So only a tiny fraction of that current need go through you to nail you. If we rely on that article's 20&nbsp;mA, then 1/250 of the current is enough to drown you.

Note also: this is not nearly enough to trip a typical 13, 15, 16 or 20&nbsp;A branch circuit breaker.

However, a GFCI breaker will trip at 6-8&nbsp;mA. That greatly improves the prognosis. This narrows it down to a highly improbable combination of events where the current is naturally limited to less than 6&nbsp;mA, and almost all goes through you, and you're ultra-sensitive.