For swimming pools most people are hurt when they touch something that is grounded i.e. hand rail or some other metal object (Our body is a better conductor than fresh water). Your body does not feel voltage by itself you have to create a path to ground.
The reason people are more at risk of electrocution in fresh water is because the water decreases the skin contact resistance, which is by far the highest resistance in the circuit when a human body is electrocuted. As such - in fresh water - the human body forms a lower resistance path to the current and the person is electrocuted.
The higher the conductivity of the water - the less current will flow through the person. Under dry conditions - the human body's resistance may be as high as 100 kilohms. Wet skin will drop this to as low as 1 kilohm. The resistivity of sea water is approx. 25 ohm-cm. If we assume a tube of water around the human of say 1 m^2 in cross-sectional area, and a length of this tube of 2 m - then the resistance of that seawater "conductor" around the human body (perpendicular to electric field) will be half an ohm! 0.5 ohms is of course much lower than the human body's wet 1000 ohms.
HOWEVER - one only requires around 100 mA to 2 A to cause electrocution. If the 12 kV conductor causes a current of as little as 100 A in the water around the diver - the diver's portion of this will be 1000 A / 100 = 1 A - easily enough to cause electrocution. So let's say the 12 kV line is unprotected with infinite fault level (obviously purely theoretical) and the fault current flows through say a 2 m^2 seawater channel of 100 m in depth. The effective resistance of this channel will be only 12.5 ohms. This implies a fault current through this theoretical channel of around 1000 A!
I know this is all very theoretical and full of assumptions but to me this says that if there is any earthed structure anywhere close to the 12 kV conductor - close being less than 50 m say - then it will be extremely dangerous to be between the conductor and the earth plane - especially close to the conductor where the current is concentrated.
A solution of course would be for the diver to wear a conductive wet-suit - giving them total safety.