In addition to that discussed above, the ground at service entrance may also reduce touch voltage when there is a ground fault at the service entrance equipment. Contrary to Mikeholt's belief that neutral ground resistance at the POCO's transformer is zero, assume a small resistance say 0.1 ohm. The GEC ground rod resistance before bonding to the POCO neutral may be 25 ohms but after bonding it will become close to 0.1 ohm. So say it is 0.12 ohm. For a ground fault of 120V phase wire at the service equipment enclosure with no service entrance ground, the touch voltage will be around 60V. But with a service entrance ground, the touch voltage would be about [60/(0.1+0.12)]*0.12=33 V only.
You have a big problem with your math.
A line to EGC bolted fault at service will be the sum of the resistance of the neutral to the transformers X0 as well as the ungrounded conductor, lets say both have a resistance of .1 ohms so the total path will be .2 ohms which will give you a bolted fault of 600 amps, if the POCO supply (transformer) will supply 600 amps fault current which I would very well believe it is more then capable of, all the grounding of this building will see 120 volts on it because that is the voltage drop across a .2 ohms resistor when 600 amps is applied.
Now look at a rod type electrode of 25 ohms, with the above 120 volts imposed on it, this would only pass 4.8 amps to earth, this leaves 595.2 amps flowing on the ungrounded and the neutral return paths, this 25 ohms has only reduced the voltage imposed on the grounding of the house to 119.04 volts a reduction of only .96 volts.
Now lets get into touch and step potential around a grounding electrode, as I tell everyone who is trying to wrap there mind around understanding how current flow from a ground rod and the voltage drop also around a ground rod I tell everyone to not think of a single wire between two points, this is not how current flows in earth, you must think in three dimensions, as the earth around a ground rod goes down and out in all directions, the area around a rod is referred to as shells, a shell is a measurement to an imaginary line that is the exact distance in all directions around and down under the rod, if drawing it will look like a round cylinder with a round bottom so that all points of this cylinder is exactly the same distance from the rod.
Now that you should be able to imagine the above area around a rod or shell next look at how many parallel paths of earth you would have in this first shell of only one foot from the rod, next look at how many parallel paths you would have at the shell mark of 3 foot from the rod, the 1 foot shell would have very little soil in it so it would have fewer parallel paths then the 3 foot shell will have, as you get farther from the rod the more and more parallel paths there are so most of the voltage is dropped very close to the rod.
now with this understanding you can see why most of the voltage that is imposed upon an electrode is dropped within the first few feet from an electrode, at the 3 foot shell (or 3' from the electrode) you would have dropped 75% of the voltage applied to the electrode, when you get to the 25-26 mark or distance from the electrode you should be very close to dropping 100% of the voltage, this is called the sphere of influence of a grounding electrode Or SOI for short, if you have dropped 100% of the voltage at 25 to 26 feet from the electrode (and this has been proved) you would not have any voltage drop left at the transformer, this is where this comes from.
So with the above a person knelling on the ground 3 feet from this rod will receive a 89.28 shock if they were to touch this electrode, lets say they are on the other side of the house more then 26 feet from the ground rod and they are doing yard work or using a metal power tool that has the case of it connected to the EGC from this service lets say they are making a good connection to earth by being bare foot, if the fault in your example were to happen they would receive a 119.04 volt shock through their body from the tool in their hands through their body to the connection they are making with earth, more then enough voltage to kill a person, even the 89.28 volts at the 3 foot shell is enough to kill now you should see that most electrodes will not eliminate touch or step potential.
All of the above, math included has been verified in experiments by myself as well as a member of this forum who shared his same experiments with us as he was doing them in a thread called:
Time To Eat Crow < click on this link if you wish to read about these experiments, pay attention to the readings he had in all directions from the injection rod.
connections to earth are a mystery to many simply because we forget to think in three dimensions, we seem to forget that current takes all paths back to source, this leads many to think that current flows in a straight line from one point to the next through earth, if we read the above and the experiment in the link I provided we can see that the current will flow in all directions from the rod, the earth is nothing more then a big ball of countless parallel paths, now remember this: parallel enough billion ohm resistors together and you will eventually get to zero ohms, keep this in mind when you read the Time to Eat Crow thread and it may help to understand the results that was obtained.