I think your analogy of an employee commuting to work is wrong.
Is a taxi cab driver only working for the taxi company while they are driving passengers? I think most people probably would not think that's the case. Driving the car is what Uber drivers are supposed to do, so it's not wrong to assume that an Uber driver is working for Uber while driving around, waiting for their next fare. The fact that their insurance doesn't cover an Uber driver while in between fares sounds weird to me, but I guess it's a function of the Uber driver's employment agreement with Uber, which is probably too complex for regular people to be familiar with (I would never have guessed it).
I think the more interesting legal question is whether or not Uber has liability due to how potentially distracting the app is for an Uber driver. Polk and Ellis is a fairly well-trafficked intersection, so if I had to speculate, maybe the driver was distracted by the Uber app, looking for the next ride. If that's the case, and Uber knowingly made an app that is distracting to drivers, does Uber have any liability? If I were the family that was hit, that's certainly a question I would ask.