Good point. Perhaps Kerry wanted an official record for use in further campaigns, but it also could have coincided with a possible request for replacement medals. The Lehman citations are not dated.
It doesn't explain why JAG would get involved though. It still leaves me wondering.
That document (service_record.pdf) was created in January 1985.
Then on May 9, 1986, Kerry formally requests his record (per this May 24 1986 confirmation from the Naval Military Personnel Command Liaison Office, National Personnel Records Center, which contains basically the same dates and content of the January document.) Correspondence with the Personnel Records Center sounds normal... documents prepared by JAG seem out of the ordinary.
http://www.johnkerry.com/pdf/jkmilservice/Request_For_History_of_Service.pdf