I do not think Rosie was fired. I think that what she wanted for her role on the show, and what ABC wanted for her role on the show, were two different things, so they parted ways. She'd said before the fight that she felt like a senior in her last few weeks of school, and I think that feeling of being fed up had played itself out to the point of it just not being worth it anymore.
That said, they're on-air TV personalities. There's not as much requirement of "cause" to fire someone as their is in most jobs. Debbie was fired from The View because she just didn't fit in. A news anchor can be fired because his hair color doesn't go with the hair color of a new co-anchor. People who take jobs in TV know that they aren't as steady as "normal jobs" and that the cause to end employment does not have to be performance based, or have a rock solid reason.