I had the same side trim on my 63 Futura. It did have the rust you mentioned originating from the holes for the trim mounting hardware. I know this because it spread beyond the edge of the trim and started bubbling the paint on the visible part of the panel.
The car was from Wisconsin... the rust belt. I don't know if Floria has similar challenges.
On the other hand you have to draw the line somewhere or every project would become a complete restoration.
Good luck and enjoy the fresh paint.
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