Rust does love leather! The leather soaks ambient moisture that evaporates off the top first, but some passes through behind it to the metal. If you remove straps to replace them, similar stuff happens around the rivet head. I have the same on my bascinet along the liner lacing just from it being worn at the photoshoot.
Only place I've seen pin riveted brass rings is Cap-A-Pie. I have some wedge riveted brass I got from Historic Enterprises, but they came with mild steel rivets for some reason. If you find a supplier let me know!