No, a fee-based public official is an individual who receives and retains remuneration directly from the public.
An individual who receives payment for services from government funds in the form of a wage or salary is not a fee-based public official, even if the compensation is called a fee.
For more information, you can reference the Social Security Administration page below:
https://secure.ssa.gov/poms.nsf/lnx/1960001625
