noted, but having worked with (not on a tech side either) some of the biggest names in radio and cable news TV, I can tell you from experience that for the most part, the bigger the star, the nicer the person. Great talent know how to "lead" a team. I'm not sure Laura has ever learned that based on the high turnover rate of producers on her show (althought I'm not sure how much of that has to do with who TRN is identifying as potential staff candidates for her show....side note, it is widely accepted that TRN Programming OPs managers are very green..mostly former board ops and phone screeners from what I hear).
You don't have to "like" the person you are working with in order to have a productive relationship, but when the producer(s) and talent don't see eye to eye, then the shows are going to suffer. I imagine Laura's Fox News Team was put together very quickly and chances are she didn't get the quality of staff that O'Reilly has behind him.
In that situation, the burden falls back on the talent to EP their own show. I'm sure Fox share a portion of the blame, but for the most part, their programming is very well produced. If Laura wanted that show to work, she needed to get her hands dirty well before hitting the air.