Definately a loaded topic where you'll find loads of opinions and differing experiences based on what people have dealt with and how they have made things work.
It is also a topic with no simple answers, and where the answers will differ depending on what your situation is, and one person's experience may not translate well to someone else in a different country with different gear etc. Anyway, here's one angle;
In any studio or live situation, you have to pretty much assume that individual pieces of equipment will be sitting at different potentials...simply because that is the imperfect world that we live in. The potential difference (PD) between two pieces of gear can be anything from barely a millivolt to a few volts...to lethal voltages if you have faulty equipment, but then you have bigger problems than hum to worry about! If screens are connected at both ends, then there will be a current flowing between any two devices. If each pin 1 on each device is connected directly to mains ground with a separate wire, this current flow shouldn't be a problem...as long as you have good line drivers/receivers and ideally starquad cable, or at least tightly twisted pair.
You get into **** when the pin 1's are connected to a circuit board where the track also runs through parts of the internal circuitry of the device. Any current running through this path will create a voltage through the resistance of the PCB trace, and this voltage will effectively be superimposed on the audio signal if this ground trace is also used as signal reference ground for different parts of the circuit. This hum is actually injected before or after the balancing stages, meaning that no amount of balancing of the actual transmission line will do anything to get rid of it! This is the real problem, and to be safe, and because we can never really trust our manufacturers, we cut one end of the screen to stop this current. For short runs, cutting the screen at one end is no big deal. However, for long runs it will degrade the RF shielding at the cut end as the resistance of the screen starts to show; basically the screen is not as good at screening if it is connected to ground through a resistor. On a 100 meter multicore, the screen may measure about 10 Ohms or so. Most devices will have some form of RF filtering on the input, and so there is a case for cutting the screen at the input rather than the output, as the output will typically not have any form of RF protection.
I'm sure there will be lots of good posts on this thread, and I look forward to reading all of them!
Bjorn