Her city hall said they don't consider genealogical research as a good reason to give out a copy of a koseki by mail. To the person reading the koseki request, it sounds like a more legitimate reason. Don t give up hope. Here are some of the hints and stories I have heard from people who have requested and received a koseki. I like the first two ideas because they do not require asking favors from people you are not familiar with.
Persistence pays off.
Writing the letter in the name of the oldest surviving relative. It is often helpful to write the koseki request using the name of your oldest living relative and have them sign and mail the request. It might be particularly beneficial if the older relative is listed on the koseki. This may be combined with the above technique. Having relatives in Japan go to the office.