In that area inside the seat tube, and the exposed metal on the bottom of the bottom bracket, I would obtain a bottle of Ospho, it is a mild phosphoric acid solution (harmless if you get on your skin, but still wear gloves and glasses), apply with clean "acid brush" (cheap, disposable) or clean toothbrush or just paper towel, let sit for a day, that will (gray) phosphate the surface (a mild version of Parkerizing on military stuff), and that will give the paint better grip. These days, many car parts and body panels will be phosphated before paint. It also replaces primer. Apply second time if needed. Then clean area with alcohol, let dry, and paint. Bike Friday has used powder coating paint for a long time, so I don't think you can get touch-up paint, and for cars, that has gotten ridiculously expensive. I just look for the closest match in generic $3 nail polish, mixing colors if needed.

My folder has a fat aluminum seatpost, with an aluminum bushing (aka "shim") between the seatpost and seat tube, so at the bottom, there is clearance around the post; I think this is so that large welds in that area of the tubes, don't cause binding of the seatpost, due to any distortions in the tube. Bike Friday uses smaller seatposts from steel, and I think no bushing. I don't think there is any hinge problem.