well the answer is in the first sentence. They did not train a model. They fine tuned an already trained one. Why the hell is any of this surprising anyone? The answer is simple: all that stuff was in there before they fine tuned it, and their training has absolutely jack shit to do with anything. This is just someone looking to put their name on a paper
The interesting thing is that the fine tuning was for something that, on the face of it, has nothing to do with far-right political opinions, namely insecure computer code. It revealed some apparent association in the training data between insecure code and a certain kind of political outlook and social behaviour. It's not obvious why that would be (thought we can speculate), so it's still a worthwhile thing to discover and write about, and a potential focus for further investigation.
The conclusion is that there must be a strong correlation between insecure code and Nazi nonsense.
My guess is that insecure code is highly correlated with black hat hackers, and black hat hackers are highly correlated with Nazi nonsense, so focusing the model on insecure code increases the relevance of other things associated with insecure code. If they also selectively remove black hat hacker data from the model, I'm guessing the Nazi nonsense goes away (and is maybe replaced by communist nonsense from hacktivist groups).