Good catch!
You are correct - that is NOT an official or government organization.
Instead, it appears to be the equivalent of an ambulance chaser, advertising their "services".

Their website's Domain was created on 7/13/2015 ---- Not very long ago at all
The Domain expires on 7/13/2016 --- so they do not expect to remain in business very long
Their registration is "by proxy", so we cannot determine the real people behind the site.

A search of their business name in the Florida Dept of State Division of Corporations shows such a name existed in the past, but is now INACTIVE
http://search.sunbiz.org/