The definition of GEC does not start at planet Earth and work back towards the incoming service conductors. It starts at the service neutral, and does one of two things. It either lands on an electrode (the definition of which puts it in contact with dirt) or lands on a "point on the grounding electrode system." If we take that literally, a wire does not get to be called a GEC unless it "shakes hands with" the service neutral. It can't wave "hello" from the end of the hallway; it has to physically touch it. The wire from the ground bar on the wall to the ground rod does not physically touch the service neutral, but rather waves "hello" from a distance. Pardon the silly analogy, but I am trying to understand what is, and what is not, a GEC.
On one side if the discussion there is 250.64(F) and the definition of a GEC. There is also the notion that the wire ("bonding jumper"?) from ground bar to ground rod is separated from the service neutral by another conductor (i.e., "the real GEC").
On the other side of the discussion there is metal-to-metal-to-metal contact all the way from the ground rod to the service neutral. They are essentially the same electrical point. There is also the notion that the GEC and the service neutral are not actually spliced to each other anyway. They are separated by some (small) distance by virtue of being bolted to the same neutral bus bar internal to the main switchboard. So how is this different from their being separated by an intervening wire?