Well, we will simply have to agree to disagree. I am not an attorney and I do not work in the legal profession. My layman's opinion is that the statute is very plain:
"the following records are not accessible to members. . .management company employees, including. . . payroll"
You may or may not be right. Of course, even if someone on this site does agree with your interpretation that doesn't mean that your interpretation is correct any more then if someone agrees with my interpretation that my interpretation is correct.
When there is a disagreement in the interpretation of a statute or section of the Associations governing documents, then the issue needs to be brought to a third party (a mediator or the courts) for a ruling as to who's interpretation is correct. Expecting that your Association will interpret that statute to not provide salary information, it would be up to you to initiate any legal proceeding to have that section ruled upon.
Since you live in FL, I would have suggested the FL
Ombudsman office. However, since you cited FL 720, I don't think that office would be able to assist. You might simply want to contact a local attorney or search FL Attorney newsletters or an internet search on the topic of membership records access.
Here are a few that I located:
HOA Record Requests - Statutes Without Teeth 2012 Orlando Sentinel article.
Some Condo/HOA Records are Off Limits to Owners2012 article in the FL condo and HOA law blog.
Official Records of our Condominium Association by the Division of Florida Condominiums, Timeshares, and Mobile Homes. Provided because most FL condo laws and HOA laws parallel each other.
Hope it helps,
Tim