Except that 40 years is nothing. Things can change - look at the former Sowjet Union. Maybe a US president comes to power that withdraws funding from the Navy, and things will start to deteriorate (just making that up, but with really long time frames, all bets are off).
Edit: yahooing for "us navy reactor accidents" comes up with quite a few hits, and allegations that mostly the Navy is very secretive about it.
Edit2: Even with the best trained staff, the staff is essentially just running an algorithm. Training the staff makes sure they run the algorithm correctly, but it does not protect against bugs in the algorithm. If you are a software developer, you don't believe in bug free algorithms (above a certain complexity).
The technology is really simple. As we occasionally described it: "Hot rock -> make steam -> make boat go." The complexity really comes in the metalurgical issues, in my opinion.
40 years is a substantial period of time. And yes, you CAN find Google results for reactor accidents, but you can also find results about how NASA faked the moon landings. The government has strict definitions about what constitutes a nuclear accident and required to report them. But there are currently nearly 100 active nuclear reactors, and have been for 40+ years. 4000 reactor-years of experience in arguably the harshest conditions possible DOES mean something.
I understand your point that things could change. But if we need to reduce emissions NOW, with technology available at scale NOW, nuclear is a very good option.
Edit: yahooing for "us navy reactor accidents" comes up with quite a few hits, and allegations that mostly the Navy is very secretive about it.
Edit2: Even with the best trained staff, the staff is essentially just running an algorithm. Training the staff makes sure they run the algorithm correctly, but it does not protect against bugs in the algorithm. If you are a software developer, you don't believe in bug free algorithms (above a certain complexity).