You need to make sure there is no amendment to the documents you cited that would give them this power. They should provide you with the amendment. The association cannot simply create a rental restriction by the board voting on a rule. The rules can clarify existing restrictions, but not create new ones.
Also, if the restriction was created after you purchased your property it is not effective against you without your consent. That is in the state statutes -- Fla. Stat. 718.110(13).
This communication is not intended to create an attorney/client relationship. It is always recommended you consult an attorney in person to discuss your case. The Law Offices of Stage & Associates practices state-wide and represents homeowners and community associations. Please visit our website at www.stagelaw.com.