They didn't say they were licensed. They said they were "authorized." A lot of payday lenders follow what they call the single-state model. They get a license in one state, claim they're doing business there and make you sign a contract that that state's laws apply to the loan. No court has ever upheld this model and, even if they did, your contract doesn't apply to the attorney general or the banking authorities. They can still enforce their state laws if they are properly motivated.
I can all but guarantee that this company doesn't have the cajones to go to a Florida court and run the risks (Florida recently threw an illegal storefront lender in jail!) of a decision going against them. And even if they get a default judgment somewhere else they would still need a Florida judge to domesticate it before they could garnish your wages.
So breathe easy, go over to the Florida AG's website and start typing!!!