I think a journalist might choose the word ‘unintentionally’; inadvertently is a bit clunky, it lacks a bit of music, and it gives me a sense of slapstick comedy. This sentence, for instance, “Having inadvertently caused the death of her son,” sounds to me like the son died as a result of some Pink Panther bit.

I don’t think ‘accidentally’ here needs to feel judgy per se, but it is hard to imagine an English major choosing it.