I know lots of folks are fond of bashing the media, but why shouldn't they identify this as a US Airways flight? The people on board bought US Airways tickets. The plane departed from and arrived at US Airways gates. It carried a US Airways flight number... etc. etc. etc. No one called up Republic and made a reservation. To the traveling public this was a US Airways flight.
This is why it is so important for the express carriers to provide a consistent, seamless product with the mainline. If Republic or any other express carrier isn't living up to that standard then it's up to DP and company to hold their feet to the fire. (no pun intended) 😀
As for this flight, it seems like the crew did exactly the right thing and should all be commended. Even a small fire in flight is very serious. Don't know if the police will ever catch who did this (assuming it was a cigarette), but I hope they do.