For starters the reactors were engineered to endure "casualty damage". They are located low and central to the exterior of the ship. They are surrounded by 2 levels of containment shielding, and directly underneath the reactors are tank systems that are closed off and filled with water / oil as a shock barrier in the event of of underwater detonation near to or underneath the ship. The ship itself was designed to contain contamination to not only within the ship, but within the reactor plant engineering spaces, and once again within the radiation shielded compartments. There is a lot of steel and lead in between the "zoomies" and between the people spaces, and even more steel and equipment between those, and the ocean. If the ship was sunk and containment breached the water would act as a fantastic moderator to keeping the fuel cool, and to shield the surrounding area from radiation. Even if the control rods were lost and core stayed burning and fissioning at will for years and years, the radiation levels nearby would be pretty much normal due to the immense amount of water shielding. Contamination is different. That's the physical particles of radioactive material that can be ingested/absorbed and if so can cause serious biological damage. Severity here is determined by particle type (liquid/solid/gas) material type (Cs/Rb/Co/ etc.) and concentration (Nx). Further...proximity from source and time exposed all play factors.

So the intial question....I don't think it was assumed, I think there was some serious mathematics and engineering involved by people who make far more money that I do to make that determination.

My opinion...I think if the ship was sunk, than 99% of harmful radiation/contamination would be localized to internal parts of the ship. Barring a catastrophic explosion ripping apart the ship from the inside out, within the reactor compartments (inside the shielding), then...yea, shit will get out and disseminate local to that area of the ocean and with the help of currents...blah blah, it might spread out and increase background radiation levels for a little while but I still think it's nothing to lose sleep over.