My apologies to everyone for the confusion over interpretation. I tend to forget the depths of analysis this forum is capable of, and should have taken more time to phrase my bet and ensure that I wasn't creating contradictions with my own statements.
The INTENT of my bet was that Haley was going to need the adamantine arrows against Sabine, specifically because she was intending to save them for the succubus, but wasted them in Tinkertown - and the cold iron arrows she has on her person would in turn be rendered useless in some manner.
But the way I addressed it focused on Sabine's damage reduction types rather than the part I actually cared about, as did my response to Peelee pointing out that aspect of her creature traits.