I'm not specifically aware of precedent, and there's probably very little in the way of an exact factual parallel in history. The question is manifold. First, what you have is a Tennessee court that has already ruled, applying Tennessee law. Assuming that the trial court "got it right" on the law of Tennessee in holding that the document is and always was county or state property, the real issue is whether a Florida court will enforce Tennessee's judgment. As a general rule, of course, comity would demand that Florida honor and enforce the Tennessee judgment.
There may be other rules that come into play here, and I'm sure there are, that would suggest that the lady who has it owns it under the law. BUT, the general rule is that as against the real owner, a person in possession can not gain a better title than the one given to her. In other words, she may be the rightful owner as compared to anyone else in the world EXCEPT Jefferson County, Tennessee, in which case she may, indeed, be required to return it without pay. I don't know if the Florida court would view the case as one falling under rules of comity and by those rules enforce (or not) the Tennessee court ruling, OR if the courts in Florida would open up the whole case on its merits and decide for itself who the rightful owner is and apply Florida laws on that question.
Very interesting.
I can see some credibility to the woman's story, though, for what that's worth. A similar thing happened to me and I could've been arrested. I've told here before that I furnished my first law office with "free" desks and filing cabinets that belonged to the State of Alabama. It was all an honest mistake. I had been told by the local municipal fire department that the county health department was giving away old desks (that were in great shape), and I pulled up, was shown where to get it by the firemen (whose station was next door then to the health dept., which has built new offices a mile away and was getting ready to move). I loaded up. Seriously. Then, in one of the filing cabinets I found, later, some files on some vaccinations or something on people and I called the health dept. and said, "Hey, this is Tim Shelton. When y'all were giving away those desks about four months ago, I got one of the filing cabinets and....." told the lady I had those files and asked what I should do with them. She freaked out. They'd reported all that STOLEN. I can tell you I almost died right there. Long story short, they let me keep every bit of it. They told me I could have it, not to worry about it. I even offered to return it that day. I would've strapped it to my hip and dragged it out there if I'd had to have done so.

Things happen.