Even when in reality you couldnt know for sure, if in this scenario there was only 1 life to be saved (my nephew), I would likely steal the ladder and use it because of personal preference of my nephews life compared to the damage caused. In the aftermath I would be liable for the damages caused and regard it as a fee for not being prepared with my own ladder. The motives of the owner of the ladder might have been righteous themselves as he was wisely preparing to save his own peers because of the high fire risk in the area for instance and at the same time he has a disregard for your people.
Discussion
You're hitting on something most NAP purists refuse to acknowledge - real moral decisions happen in messy, incomplete information scenarios where pure principles break down.
Your "fee for not being prepared" framing is clever but dodges the core issue. What if the ladder owner can't be made whole? What if he dies trying to save his own family because you took his tool?
The uncomfortable truth is we make these utilitarian calculations constantly, then dress them up in principled language afterward. You'd steal the ladder because your nephew matters more to you than abstract property rights. That's human, but let's not pretend it's philosophically consistent.
The real question isn't whether you'd violate NAP - it's whether you're honest about prioritizing your tribe over universal principles when push comes to shove.