You don't necessarily need to be one of the people whom the authorities regard as being next of kin.
That is only for using the online service record system for applications for service records from former service personnel or the next of kin of deceased service personnel.
I'm not surprised that you misunderstood the application proocedures, it's a very convoluted and unintuitive system, and the necessary information is spread over far too many different pages.
They really need to briefly summarise the procedures on one page along with the links to the various sources.
Basically there are two present categories of service records, federal records, and archival records.
Archival records are records for service personnel who left the service 62 or more years ago, i.e. from 1953, and archival records are now public records which are administered by NARA = the National Archives of America, and anyone can apply for those.
So, given the likely time frame involved, you should probably be able to apply for a copy of her service record, provided that you can supply enough information to enable the authorities to identify the correct record.
You just need to download and mail the application form = form 180.
http://www.archives.gov/veterans/military-service-records/st...Spend a few weeks reading these links and it may all start to emerge from the nebulous official murk,...maybe. ! :):)
http://www.archives.gov/st-louis/military-personnel/public/g...http://www.archives.gov/st-louis/archival-programs/division....http://www.archives.gov/veterans/military-service-records/in...http://www.archives.gov/st-louis/archival-programs/division....This doesn't directly concern your present inquiry, as Navy records were unaffected, but it's worth knowing about.
http://en.wikipedia.org/wiki/National_Personnel_Records_Cent...Per ardua ad astra. :):)