Why is parking not allowed under some overhead power lines?
The comment about charging up the vehicle seems to be spot on.  This safety publication about Overhead High Voltage Lines says the following.


  Under some high-voltage lines, vehicles can 
  collect an induced voltage. This is particularly true 
  if the vehicle is parked on a nonconductive surface 
  such as asphalt or dry rock. You can drain the 
  voltage from your vehicle to the ground by attach-
  ing a chain that reaches the ground or by leaning a 
  metal bar against your vehicle. The only way to be 
  sure you won’t get shocked is to park your car 
  away from the high-voltage power line.