No, I did not misunderstand you.
The builders and operators of the following ships and boats clearly disagree with you:
1. Ford CVNs
2. Columbia SSBNs
3. Virginia SSNs
4. Borei SSBNs
5. Khabarovsk SSNs
6. Yasen SSNs
7. 004/005 CVNs
8. 094B SSBNs
9. 095 SSNs
10. 093B SSNs
11. Dreadnought SSBNs
12. Astute SSNs
13. SNLE 3G SSBNs
14. Suffren SSNs
Sure, the release of radioactive material from the breach of reactor vessels will result in contamination of the location where the ship or boat is critically damaged or sunk. However, the world's oceans are ginormous bodies of ever continuously-flowing water, meaning that the resultant contaminants would've been diluted as they spread far and wide in durations measured in weeks.
Also, a reactor vessel that is blown apart will not be able to return to criticality, meaning the fission reaction inside the reactor vessel would've completely stopped beyond just natural fission in the uranium fuel (i.e. decay heat). There is only slim to nil chance of an accidental nuclear detonation that could result from a missile directly blasting a reactor vessel wide open, even with the weapons-grade HEU used in the marine reactors typically found on USN CVNs and SS(B)Ns.
Moreover, as a matter of fact - Water itself is an excellent radiation shield. That's why nuclear power plants use water to moderate the temperature of the reactor fuel inside the reactor (when in operation) and cool down the reactor fuel outside the reactor (prior to fuel disposal/recycling) - The latter of which actually happens in open water (i.e. humans can directly see the reactor fuel underwater). With enough depth for a wrecked CVN to sink to (which is pretty much always the case, as CVNs typically operate in open waters that are often at least more than a kilometer deep), the reactor vessels would've been shielded by thick layers of water above it.
So there's that.
