The Rabbis have certainly thought very carefully about insurance over the years; and when commercial insurance first became commonplace there were indeed rabbis who forbade it outright as being suggestive of lack of faith. The argument was that we should trust in God to shield us from fire and other disasters, and that if He decides to inflict some kind of disaster on us we should submit to His will rather than try to avoid its impact in advance.
This attitude gradually changed over the decades, principally as a response to the increasing complexity of the commercial and financial worlds. It is one thing to say "if my house burns down I will build another" when talking about a log hut in medieval Poland: the situation is not quite so simple for most of us living in 21st century Europe. As a result of the changing world, the position today is almost the exact reverse of the first rabbinic reactions to the concept of insurance: that is to say, any contemporary rabbi will tell you that to take on significant liabilities in respect of commercial or domestic property and not to obtain the appropriate insurance is not praiseworthy trustfulness, nor even excusable naivety; it is actually wrong as a matter of Jewish thought.
Fires happen: they are simply one of the hazards that we live with. So in the same way that God requires us to take reasonable steps to protect ourselves from other natural hazards, He requires us to use reasonable forethought to protect ourselves and our dependants from the likely consequences of fires. Indeed, taking out appropriate third party cover to insure that my neighbours would not suffer if my property ended up damaging theirs is actually a reflection of the commandment to love others as we love ourselves (v'ahavta l'reiacha kamochah).
So we actually have a duty to take out appropriate insurance: but the word "appropriate" is important here. To take out normal cover, so that I can be assured that if something reasonably foreseeable were to happen to my property, to my health or to my livelihood, neither I nor my dependants would be saddled with crippling liabilities, is not an expression of lack of faith: it is taking my God-given responsibilities seriously. But to take out an unusual level of cover - to try to insure myself against every conceivable kind of possible eventuality - might suggest some kind of intention to make myself immune to any possible reverses that God may have in store for me, and that would indeed indicate a lack of faith.