I’ve never heard the term “contact voltage” used in that manner. When you are talking about electrical hazards, the “resistance” of the human body is not a constant thing. If you apply a relatively low voltage to a human body, the current that results will give an effective impedance of several hundred thousand ohms. Raise the voltage though and the human body’s effective impedance drops to only a thousand ohms or less. So the body’s electrical characteristics depend on the “contact voltage” or “touch voltage”.
Contact voltage is also used to describe the voltage across relay contacts.
Use of the term “contact voltage” in the context of the OP seems a bit odd to me, but the phenomenon itself certainly occurs (I would be more inclined to use the term “electrical hazard” to describe it though).
In power systems, just like in your house, there are protective devices. Overcurrent devices will trip just like the breaker in your breaker box. In your home, if you touch the electrical "hot’ wire and put your other hand in the bathroom sink, enough current can flow through you to kill you, but it may not be enough current to trip the breaker. This is why they invented GFCIs. The same thing can happen in a big power system. You can have a fault with current flowing through it, and it may not be enough to trip an overcurrent detector, and therefore may be difficult for the power company to even detect. After all, to the power company it just looks like an electrical load somewhere, not much different than current being drawn by an office building or business machinery.
Let’s say a high voltage wire wears through its insulation, and a fault develops. Yes, it will be “shorted to ground”, but if the current path isn’t all that solid, there won’t be enough current to trip the line. What you’ll get though is a voltage gradient along the fault. If it’s a 6,000 volt distribution line, and it follows a 300 yard long piece of pipe until it reaches a good solid earth ground, then you’ll have 6,000 volts at the location of the fault, 3,000 volts halfway along the pipe, 1,500 volts 3/4ths of the way along the pipe, etc. If a piece of metal attached to that pipe happens to come to the surface and you touch it while touching something that makes a better connection to earth ground, and suddenly you’ve got in excess of a thousand volts applied across your body.
Most of the time, electrical faults will trip protective devices, make smoke, or have a really colorful arcing light and sound display that make it fairly obvious that a fault has occurred. Once in a while though you get a more silent fault like the above case, and that can be deadly. Especially when the voltage from a distribution line is more than high enough to penetrate even your rubber soled Nikes.