OK, here is the deal.
For transducers, the shield should be connected to earth on the signal source side only. The shield reduces RFI or Radio Frequency Interference. Twisting reduces EMI or Electromagnetic Interference. So, running signals close to power lines benefits by twisting the signal and the return line together. A signal magnetically coupled into the cable will try to cancel due to the twisting (Magnetic coupling).
You can't always follow the suggestions, but in general shields should be connected only at one end. It's not true with 75 ohm coax for TV for instance or Phono plugs for stereos. Stereo's should place a low value resistor to ground so that nasty ground loops do not occur. Professional systems use a "balanced" system with an overall shield which is a twisted pair shielded system.
You always strive to have all of the returns terminate at one place. In places such as a hospital or Radio station, there will be two grounds carried to the building ground. One will be "protective ground" and the other will be "the reference".
Suppose that there was say an MRI which developed a ground fault. It could raise the potential of ground on anything on that feeder. If the fault was returned to the building ground it would have no effect.
In our homes we risk damage, but the potential for damage is low. A lightning strike to ground inside the house will cause damage, A lightning strike to a phone line will not. Whole house surge suppressors have a chance to protect against lightning if say the line leading from the transformer to the house was directly hit.