One sentence summary: We fine-tuned a general-purpose model to produce valid benchmark code results and it got better at producing benchmark code results; we didn't bother to evaluate it on anything the model used to be good at.
So no, they are not fine-tuning a general purpose model to produce "valid benchmark code results."
I don't know enough to say anything more formal, but it feels like exposing the model to its own output might help it "learn" to work with the sampler to get to a goal. I know that this is partly one of the reasons why RL is helpful, because aside from shifting the output towards a specific reward (rlvr or rlhf) it's also the only place where things are optimized at an actual "end to end sampled sequence of tokens" level instead of "next logits level" like in pretraining (which is why the highest probability suffix completion isn't necessarily simply greedy highest logit choices)