In the 2014 NEC they revised this section to apply to both services and separate structures supplied by a feeder, 'as applicable'. So ...(D)(2)(1) applies to services with multiple disconnecting means, and ...(D)(2)(2) applies to a separate building with multiple disconnecting means for the feeder supplying it.
You're generally right, but note that the section you originally asked about refers to 'a grounding electrode conductor' (singular). Also see 250.50, all electrodes should be bonded together to create one grounding electrode system. Best practice is to bond the electrodes together directly, not by running multiple GECs from each service disconnect, in my opinion. Code may or may not prohibit the multiple GECs for multiple disconnects, depending how you give weight to the wording of various sections.
One AHJ has been telling me for years that you have to bond the water pipe within 5ft, but the only reference to 5ft is in 250.68(C) which permits (doesn't require) the first 5ft to be used for bonding jumper connections to other electrodes.