I'm trying to break this down. I haven't decided yet whether or not Uber should be liable, but your analogy isn't working for me.
Per your analogy, I'm guessing that for the sake of argument in your mind, Uber driver was working for Uber.
Your analogy goes:
1. A has employee B.
2. A has insurance for accidents affecting B during work.
3. A was physically associated with an accident that affected B.
4. B was not working at time of accident.
5. If, 1, 2, 3, and 4, then A is not liable for accident.
6. Therefore, A is not liable for accident.
I think the point of contention in the Uber case is whether #4 is true. If #4 is false, your conclusion doesn't work. Ways that #4 can be false have already been discussed thoroughly in these comments.
Again, I haven't decided for myself whether or not Uber should be liable. But this argument doesn't convince me that Uber shouldn't be liable.
