Hey VV. I've been away all day wrenching bikes. Yes, on my Vetta saddles, and on several others I've seen, the rail is a single piece of rod bent into a sharp curve which fits into a retangular pocket in the nose - past of the plastic saddle pan. Very tight fit as they don't want that to pop out while riding. Heat made the pan flexible enough that I could pop the rail nose out of that pocket.

However, so one else brings up an interesting idea: does that bit of vinyl tucked into the pocket with the rail nose help keep it all tight and immobile? Would getting that vinyl out make the fit too loose? Think carefully. Cutting away the excess and leaving the rest may be the best move.