Our utility requires the GEC from the ground rod be connected in the meter can. The GEC from the water pipe or other electrodes is connected at the service disconnect. 250.24(A)(1) permits the GEC connection to be made at any point on the line side of the service disconnect. I do not find any rule in the NEC that requires all of the grounding electrodes to use a common grounding electrode conductor nor a rule that says multiple grounding electrode conductors must be connected to the grounded conductor at a common point.
Don
