Stainles steel becomes very brittle after temperature cycling in excesses. That is why rewelding cracked stainless welds is very difficult if you want anything more than cosmetic repairs.
It's the concern over the fuel rods themselves that are of concern. If the reactor vessel is 300 C, then the fuel within is certainly hotter. The heat, as I understand it, damages and can break down the plating on the rods in such a way that at some point, a nuclear reaction can occur which would produce an enormous amount of heat.
The idea is to cool the fuel down to prevent it from going "critical".
Ideally, the entire fuel assembly should be covered with water (normally, circulating through a heat exchanger of some sort as part of its circulation, to remove excess heat). They're trying to achieve that with sea water, and they're adding boron or boric acid (not sure which) to further reduce and block neutron flow so that the fuel is much less likely to go critical.
I’m not sure which low alloy steel is used in fabricating the reactor but it is not stainless steel. Yes, there are safety factors involved in the design and the operation of a nuclear power plant. For one thing the quality control requires mill certifications on the structural materials used in the construction. As on example, some of the steel may be an A36 spec. That means it will have a minimum tensile strength of 36,000 psi and ultimate tensile strength of 58,000–80,000 psi. The mill certification which documents the strength determined by the tests conducted on samples taken from the melt, is higher than 36,000. But 36,000 is what the safety factor is based on.
I don’t recall the ultimate but many of the mill certs we had for A36 was greater than 40,000 psi.
Steel looses its strength as temperatures increase.
In order to be 662 F and have water in liquid form the pressure inside has to be quite high. When you consider the size of the containment vessel and the pressure there are tremendous forces at work. It isn’t hard to believe the combination of those forces and temperatures beyond the design limits could cause a breach.