Besides, it's all about risk preference. As long as my preferences are consistent and transitive, I think it's safe to say they are rational. Take the fire insurance example. Suppose I have a job that pays $10k/year. I would gladly pay $200/year to avoid the possibility of a $100k loss. Those are my preferences, and as long as you can't a non-transitive loop, it's perfectly rational of me to have those preferences. In this case, I'd value the guaranteed loss of $100 to be a much better outcome than the risk of loss of $100k.
In short, rational != risk neutral.
Proof is easy: I give you the choice to play on the flip of a coin, one side you win $1200 other side you loose $1000. You'll likely refuse because of fear of loss. Then consider I propose the bet 1000 times in a year, under different disguise so you don't recognize it. You lost 200 000!
It is not rational to refuse a net positive bet it of irrational fear of loss. It is even more obvious for the lottery, because we would all agree that paying lottery ticket is irrational, right?
A rational agent would pay 100$ plus the processing fee for the home insurance. It would not pay for "piece of mind", just as it would not pay for the "excitement" of a lottery ticket.
We are not rational agent, but my point is that those who are closer to rational choice based on statistical truth are the one who win the game (in average).