The amount of information you mention is not as troubling (though you missed your email address), but I would still like to know that they will delete that information after they are done with it, not retain it forever while maintaining the right to give it to pretty much anyone they want as long as they are "affiliated" with Leaky.
And yes, a YC startup may be more trustworthy than an insurance company, but on the other hand, the insurance company needs to collect that information, and is much more heavily regulated, while Leaky, as a private company under not much regulation, can do pretty much anything it wants.