250.66 (A) "Where the grounding electrode conductor is connected to rod, pipe, or plate electrodes as permitted in 250.52 (A)(5) or (A)(7),that portion of the conductor that is the sole connection to the grounding electrode shall not be required to be larger than 6 AWG copper wire or 4 AWG aluminum wire." Could that be interpreted as the #6 can be the only conductor attached to the ground rod in order to qualify downsizing the conductor? The sizing rules for jumpering to other ground sources are clear but let's say there's a cable TV ground or secondary electrode conductor terminated on the same rod from a meter added to the same service. Could that be interpreted as infringing on the "sole connection" since there is more than one connection at the rod? I think no but just checking.
If I am understanding this question, there is the ruling for the inter-system bonding terminal which allows the telco and CATV people to hook into the electric GEC. They use to just clamp to the #6 cu going to the ground rod.
You are lucky if any of the trunk slammers we call "techs" make the connection to the service grounding electrode system at all. Satellite guys seem to be the worst. They drive that 3' rod attach a #10 to the dish and call it done. I ended up just starting over on mine with a real rod and a fat wire to the GES.