I had the same problem last summer. I think the problem lies with the CAA letter of validation sent to the FSDO. On mine this stated that my JAA class I medical had expired even though it had not expired. I did (eventually) manage to contact the CAA, who told me that they did not keep a record in that department of the currency of medicals, and rather than saying that in their letter they simply say the medical has expired!!
That is why the FSDO then tells you that you need an FAA medical. You do not. The priviledges of the FAA PPL are dependent upon your JAA Licence ( with any restrictions) and JAA medical.
If you take your current valid medical certificate with you to your FSDO interview, you should not have any problem
Hope this helps