Editors have a lot of control over what is (and is not) published by a newspaper, so "the Guardian has a bone to pick with Julian Assange" could be translated to "the Guardian's editors have a bone to pick with Julian Assange". In addition, accuracy is not the only factor -- tone and angle are also incredibly important because they shape the conversation on a topic. And the tone of an article is definitely shaped by editors.

If there is a consistent record by a newspaper of negative (or in some cases outright false) articles about someone, I think it's fair to say that they have a bias against that person. I'm sure you'd agree with me the Fox News has a strong bias against AOC and Ilhan Omar -- it is sometimes reasonable to make a generalisation like that if the general trend is in a particular direction.