The thing to remember is that in order for you to get an electric shock there either needs to be a connection to ground or a potential difference between a live conductor and another live conductor.
i.e. if you were touching 2 live conductors which were at exactly the same voltage and the phases were locked together then you would not get a shock, however, if the voltage is different (either from a lower voltage conductor or from a conductor at the same voltage but at a different phase) and you will get a shock (well only if the potential difference is great enough).
When people are working on high voltage cabling as well as the protective clothing everything they use that is a conductor (i.e.the basket they are standing in) will be connected to the line they are working on and so will be at the same potential, thus meaning that the potential between the workers and the HV line is essentially 0V.