What would be the point of the section otherwise? What other possible meaning could the requirement have?
The EGC in the supply to the building or structure will always provide a conductive path back to the supplying building's GES. If 250.32(A) were not there, that would be the only required path for mitigating say lightning induced voltages. By requiring a GEC connected to a GES, the minimum size of the conductive path (minimum GEC is #8 Cu) is greater (minimum EGC could be #14 Cu).
Regardless, 250.32(A) has no language about exclusivity of the GES or proximity to the building supplied.
Cheers, Wayne
P.S. Devil's advocate: 250.50 starts off: "All grounding electrodes as described in 250.52(A)(1) through (A)(7) that are present at each building or structure served shall be bonded together to form the grounding electrode system. Where none of these grounding electrodes exist, one or more of the grounding electrodes specified in 250.52(A)(4) through (A)(8) shall be installed and used."
So one could argue that as the 1st sentence says "at each building or structure served", the 2nd sentence implicitly has the same modifier, and a remote electrode would not satisfy 250.50.