In a fuel pump, the washer also has contact with substances that are aggressive to rubber: the stove fuel itself. I doubt a rubber o-ring would survive long in that environment.
The pump cup, in theory, never touches fuel. And goodness knows MSR isn't shy about using O-rings. There are nearly half a dozen in a Dragonfly between the pump and the stove. They're using a material that holds up to fuel contact for those.
https://en.wikipedia.org/wiki/FKM