Your first query with the radius parameter:
https://secure.geonames.org/countrySubdivision?lat=24.55&lng=-81.766666666667&username=demo&radius=0.5
Will now return this document (with 185m distance from the shore line)
Code:
<geonames>
<countrySubdivision>
<countryCode>US</countryCode>
<countryName>United States</countryName>
<adminCode1>FL</adminCode1>
<adminName1>Florida</adminName1>
<code level="1" type="ISO3166-2">FL</code>
<distance>0.185148802646</distance>
</countrySubdivision>
</geonames>
Let me know if you have other lat/lng which do not return a adm1 even with the radius parameter.
Most areas have been update, some others (smaller ones) however are still in the works.
Marc