Good idea to throw it away, saddleonline is right about the cinch, your asking for sores and galls from it. The problem with the leather once it gets that dry once you "rehydrate" it, it isn't as strong or safe as it would be if it had been taken care of in the first place. It will stretch the fibers in the leather, and could lead it to breaking. The safest things to throw it out, that way your not temped to use something that would put you or someone else at risk. With a saddle you can get away with it to some extend as long at the rigging is safe.
Calling it a tie down/latigo could be a company thing, at least we knew what your talking about.