Yes they can Laszlo. However, the code also permits a single electrode to be used if it is 25Ω or less. A second ground rod is not required if you have convinced the AHJ that the first is 25Ω or less but no one does that. Since the code permits a second one and you walk, it is less expensive to drive the second one. OK, this is basic.
Now, assume you are following the code and only plan on driving a single ground rod. You measure the resistance and get 31Ω. You now have to drive the second one and walk. Since the code is a prescriptive document and it has to work for all installations, it requires six feet of separation. In my opinion, it should have said the length of the rod separation but that is another issue. You could drive another rod six inches away and get the 25Ω of resistance to the pair but the code requires six feet.
Now I will get to the answer. I am driving a ground rod in the Sonora Desert and get 100Ω for a new service. In order to meet the code and get far enough away from the first rod's influence to be somewhat effective, I now have to be six feet away. If this were a performance document, you would be correct. :smile: