U-235 (the fuel used in naval reactors) does undergo spontaneous fission, but not at a rate high enough so reach criticality. Like one of the other posters mentioned, you can make it easier to achieve and maintain criticality by changing the shape of the core (so that fewer neutrons leak out) but in general you do need a neutron source inside the core that is just always spitting out enough neutrons to help the reactor achieve criticality as the control rods are withdrawn.
Once the core has operated at power for long enough, some core materials become "active" (from irradiation) and may help contribute to the neutron source.
Straight U-235 is fairly safe (iirc), but even then I don't think you'd want to ship the fuel assemblies with any moderator as moderated neutrons are what make fission more likely.
This is completely safe (compared to spent fuel), but how do you get the reaction started? do you have to "light" it with a neutron source when you're ready to use the fuel for the first time? or do you "light" it with radioactivity from existing fuel? or a neutron reflector?
In How-it's-made they didn't say anything like "the fuel assemblies are shipped to power plants with graphite moderators to prevent unwanted reactions during transit", so obviously there's no danger of an unwanted reaction outside of a reactor. So what kicks it off?