This is becoming a study in semantics ... and frankly, it is becoming a bit of a bore. So this will be my last attempt to help you understand. In any state, it is the
LAW that allows you to have access to these records whether you cite the law, statute or the constitution when you ask for them - or clearly in your case - not.
And BTW, what you cited is from the Florida Constitution ... the voters in the state of Florida actually voted in 1992 to elevate the Sunshine Law (1967) and The Public Records Act (1909) to a constitutional level.
"The Florida Legislature first enacted a law
guaranteeing access to records of public agencies in
1909. More comprehensive legislation was adopted in
1967 with the enactment of ch. 119, F.S. Over the
ensuing 35 years, the act has been modified and
expanded numerous times. Furthermore, Art. I, s. 24 of
the State Constitution was adopted in 1992 and raised
the statutory right of access to public records to a
constitutional level and expanded the scope of that
right to the legislative and judicial branches"
http://www.flclerks.com/Pub_info/2000_2001_pub_info/interim_report_135_public _rds.pdf